Google App store success prediction

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install.packages('caretEnsemble')

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install.packages("highcharter")

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install.packages("stringr")

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install.packages("xts")

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install.packages('psych')

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install.packages('Amelia')

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install.packages('mice')

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install.packages('GGally')

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install.packages('rpart')

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install.packages('normalr')

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install.packages('cluster')

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install.packages('HSAUR')

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install.packages('fpc')

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install.packages('e1071')

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install.packages('klaR')

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install.packages('caret')

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install.packages('MASS')

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install.packages('randomForest')

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install.packages('class')

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library(tidyverse)

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library(highcharter) 
library(lubridate)
library(stringr)
library(xts)
library(magrittr)
library(dplyr)
library(caretEnsemble)


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library(psych)


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library(Amelia)

Loading required package: Rcpp
## 
## Amelia II: Multiple Imputation
## (Version 1.7.6, built: 2019-11-24)
## Copyright (C) 2005-2019 James Honaker, Gary King and Matthew Blackwell
## Refer to http://gking.harvard.edu/amelia/ for more information
##

library(mice)


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library(GGally)

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library(rpart)
library(normalr)
library(cluster)
library(HSAUR)

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library(fpc)
library(e1071)
library(klaR)

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library(caret)
library(MASS)
library(randomForest)

randomForest 4.6-14
Type rfNews() to see new features/changes/bug fixes.

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library(class)

Load data

dataOriginal = read.csv("C:/Studymaterial/Big Data/Project/datafinal.csv")
data = dataOriginal[,]
str(data)

'data.frame':   267034 obs. of  11 variables:
 $ App.Name       : Factor w/ 244381 levels "'N' Word Button",..: 74458 224365 168534 91457 153439 191378 242260 213421 86839 29077 ...
 $ Category       : Factor w/ 50 levels "ART_AND_DESIGN",..: 13 48 43 13 13 13 48 13 48 13 ...
 $ Rating         : num  4.55 4.4 3.66 4.11 4.65 ...
 $ Reviews        : int  305034 1207922 1967 389154 2291 2559 421918 142618 85 67514 ...
 $ Installs       : Factor w/ 21 levels "0+","1,000,000,000+",..: 13 9 10 6 7 10 6 13 7 13 ...
 $ Size           : Factor w/ 1236 levels "1,000k","1,001k",..: 1236 1236 29 147 1236 241 1236 1236 447 1236 ...
 $ Price          : Factor w/ 488 levels "$0.56 ","$0.67 ",..: 488 488 488 488 398 488 488 488 488 488 ...
 $ Content.Rating : Factor w/ 6 levels "Adults only 18+",..: 2 2 2 2 2 2 5 2 2 2 ...
 $ Last.Updated   : Factor w/ 2744 levels "1-Apr-11","1-Apr-12",..: 1936 1936 1166 1316 9 1936 1853 2180 125 2530 ...
 $ Minimum.Version: Factor w/ 84 levels "","1.0 - 6.0",..: 84 84 78 68 84 78 84 84 70 84 ...
 $ Latest.Version : Factor w/ 22987 levels ""," 1.0.1.6",..: 22883 22883 11187 16967 22883 20206 22883 22883 11937 22883 ...

Data preprocessing

data.clean <- data %>%
  mutate(
    # Transform reviews to numeric
    Reviews = as.numeric(Reviews),
    # Remove currency symbol from Price, change it to numeric
    Price = as.numeric(gsub("\\$", "", as.character(Price))),
    Type=ifelse(Price==0, 0, Price),
    Type=as.factor(ifelse(Price != 0, 1, Price)),
    # Eliminate some characters to transform Installs to numeric
    Installs = gsub("\\+", "", as.character(Installs)),
    Installs = as.numeric(gsub(",", "", Installs)),
    # Eliminate M to transform Size to numeric
    Size = gsub("M", "", Size),
    # Replace cells with k to 0 since it is < 1MB
    Size = ifelse(grepl("k", Size), 1, as.numeric(Size)),
    Size = gsub("Varies with device", NA, Size),
    # Last Updated to date format
    Last.Updated = dmy(Last.Updated),
    # Replace "Varies with device" to NA since it is unknown
    Min.Android.Ver = gsub("Varies with device", NA, Minimum.Version),
    # Keep only version number to 1 decimal
    Min.Android.Ver = as.numeric(substr(Min.Android.Ver, start = 1, stop = 2)),
    # Drop old Android version column
    Minimum.Version = NULL
  )

NAs introduced by coercion

data.clean %>%
    summarise_all(
        funs(sum(is.na(.)))
    ) %>%
  gather() %>%
  # Only show columns with NA
  filter(value> 1) %>%
  arrange(-value) %>%
    hchart('column', hcaes(x = 'key', y = 'value', color = 'key')) %>%
  hc_add_theme(hc_theme_elementary()) %>%
  hc_title(text = "Columns with NA values")

Clustering with value 3

data <- na.omit(data.clean)
normalize <- function(x) {
  x1 <- ((x - min(x)) / (max(x) - min(x))) * 4
  x1 <- x1 + 1
  return (x1)
}
#normalization of data
data$Size = as.numeric(data$Size)
data$Reviews = normalize(data$Reviews)
data$Installs = normalize(data$Installs)
set.seed(12345)
#k means clustering by using 3 main features taken via feature importance
k<-kmeans(data[,3:5],centers = 3, iter.max = 20, nstart = 1)
k$centers

    Rating  Reviews Installs
1 4.671437 1.001009 1.001433
2 2.874764 1.000050 1.000284
3 4.036534 1.000661 1.001831

clusterTable<-table(k$cluster)
data$classLabel = k$cluster
data$classLabel <- as.factor(data$classLabel)
clusterTable


     1      2      3 
134428  21836  98517

clustering plot

plotcluster(data[,3:5], k$cluster)

feature importance calculation

#Removed 1st(Application name) and 10th(latest version) column, 
#both the columns has more than 53 categories as a factor class, 
#because of which meanDecreaseGini can not be calculated - library limitation
columns = c(2,3,4,5,6,8,9,11,12,13)
dataNew = na.omit(data[,columns])
fit_rf = randomForest(classLabel~., data=dataNew)
importance(fit_rf)

                MeanDecreaseGini
Category              1382.87263
Rating              138768.69644
Reviews               1442.95171
Installs              1669.50528
Size                   162.76144
Content.Rating          22.20774
Last.Updated           294.11663
Type                    23.12899
Min.Android.Ver        104.86199

Naive bayes without cross validation and feature selection

split = 0.6
dataForNaiveBayes = data
set.seed(123)
trainIndex <- sample(nrow(dataForNaiveBayes), split*nrow(dataForNaiveBayes), replace = FALSE)
data_train <- dataForNaiveBayes[ trainIndex,]
data_test <- dataForNaiveBayes[-trainIndex,]
modelNBfun = naiveBayes(classLabel ~ ., data_train)
predictionNB = predict(modelNBfun, data_test)
confusionMatrix(predictionNB, data_test$classLabel)

Confusion Matrix and Statistics

          Reference
Prediction     1     2     3
         1 25899    16   346
         2 23376  8622 29120
         3  4532    49  9953

Overall Statistics
                                          
               Accuracy : 0.4364          
                 95% CI : (0.4333, 0.4394)
    No Information Rate : 0.528           
    P-Value [Acc > NIR] : 1               
                                          
                  Kappa : 0.2561          
                                          
 Mcnemar's Test P-Value : <2e-16          

Statistics by Class:

                     Class: 1 Class: 2 Class: 3
Sensitivity            0.4813  0.99252  0.25249
Specificity            0.9925  0.43690  0.92670
Pos Pred Value         0.9862  0.14107  0.68481
Neg Pred Value         0.6311  0.99841  0.66278
Prevalence             0.5280  0.08524  0.38679
Detection Rate         0.2541  0.08460  0.09766
Detection Prevalence   0.2577  0.59971  0.14261
Balanced Accuracy      0.7369  0.71471  0.58959

Naive bayes with cross validation

data_train <- na.omit(dataForNaiveBayes[ trainIndex,])
data_test <- na.omit(dataForNaiveBayes[-trainIndex,])
#Latest.updated and Latest.version has been removed, library limitation
#can not use features with factor level more than 53 categories
col <-c(2,3,4,5,6,7,8,11,12)
x<-data_train[,col]
y<-data_train$classLabel
modelNB = train(x,y,'nb',trControl=trainControl(method='cv',number=10))

Numerical 0 probability for all classes with observation 393Numerical 0 probability for all classes with observation 416Numerical 0 probability for all classes with observation 524Numerical 0 probability for all classes with observation 565Numerical 0 probability for all classes with observation 731Numerical 0 probability for all classes with observation 1048Numerical 0 probability for all classes with observation 1522Numerical 0 probability for all classes with observation 1816Numerical 0 probability for all classes with observation 1988Numerical 0 probability for all classes with observation 2048Numerical 0 probability for all classes with observation 2098Numerical 0 probability for all classes with observation 2453Numerical 0 probability for all classes with observation 2581Numerical 0 probability for all classes with observation 2654Numerical 0 probability for all classes with observation 2663Numerical 0 probability for all classes with observation 2700Numerical 0 probability for all classes with observation 2744Numerical 0 probability for all classes with observation 2948Numerical 0 probability for all classes with observation 3087Numerical 0 probability for all classes with observation 3351Numerical 0 probability for all classes with observation 3418Numerical 0 probability for all classes with observation 3429Numerical 0 probability for all classes with observation 3430Numerical 0 probability for all classes with observation 3464Numerical 0 probability for all classes with observation 3469Numerical 0 probability for all classes with observation 3627Numerical 0 probability for all classes with observation 4137Numerical 0 probability for all classes with observation 4335Numerical 0 probability for all classes with observation 4603Numerical 0 probability for all classes with observation 4868Numerical 0 probability for all classes with observation 4936Numerical 0 probability for all classes with observation 5123Numerical 0 probability for all classes with observation 5147Numerical 0 probability for all classes with observation 5171Numerical 0 probability for all classes with observation 5405Numerical 0 probability for all classes with observation 5443Numerical 0 probability for all classes with observation 5513Numerical 0 probability for all classes with observation 5549Numerical 0 probability for all classes with observation 5603Numerical 0 probability for all classes with observation 5741Numerical 0 probability for all classes with observation 6106Numerical 0 probability for all classes with observation 6126Numerical 0 probability for all classes with observation 6127Numerical 0 probability for all classes with observation 6423Numerical 0 probability for all classes with observation 6437Numerical 0 probability for all classes with observation 6477Numerical 0 probability for all classes with observation 6607Numerical 0 probability for all classes with observation 7242Numerical 0 probability for all classes with observation 7319Numerical 0 probability for all classes with observation 7352Numerical 0 probability for all classes with observation 7546Numerical 0 probability for all classes with observation 7565Numerical 0 probability for all classes with observation 7758Numerical 0 probability for all classes with observation 7759Numerical 0 probability for all classes with observation 7761Numerical 0 probability for all classes with observation 8057Numerical 0 probability for all classes with observation 8128Numerical 0 probability for all classes with observation 8130Numerical 0 probability for all classes with observation 8317Numerical 0 probability for all classes with observation 8434Numerical 0 probability for all classes with observation 8445Numerical 0 probability for all classes with observation 8492Numerical 0 probability for all classes with observation 8495Numerical 0 probability for all classes with observation 8554Numerical 0 probability for all classes with observation 8557Numerical 0 probability for all classes with observation 9093Numerical 0 probability for all classes with observation 9348Numerical 0 probability for all classes with observation 9506Numerical 0 probability for all classes with observation 9614Numerical 0 probability for all classes with observation 9650Numerical 0 probability for all classes with observation 9652Numerical 0 probability for all classes with observation 9658Numerical 0 probability for all classes with observation 9749Numerical 0 probability for all classes with observation 9826Numerical 0 probability for all classes with observation 10008Numerical 0 probability for all classes with observation 10061Numerical 0 probability for all classes with observation 10078Numerical 0 probability for all classes with observation 10115Numerical 0 probability for all classes with observation 10151Numerical 0 probability for all classes with observation 10198Numerical 0 probability for all classes with observation 10295Numerical 0 probability for all classes with observation 10859Numerical 0 probability for all classes with observation 11120Numerical 0 probability for all classes with observation 11126Numerical 0 probability for all classes with observation 11212Numerical 0 probability for all classes with observation 11357Numerical 0 probability for all classes with observation 11484Numerical 0 probability for all classes with observation 11700Numerical 0 probability for all classes with observation 11706Numerical 0 probability for all classes with observation 11967Numerical 0 probability for all classes with observation 12219Numerical 0 probability for all classes with observation 12488Numerical 0 probability for all classes with observation 12562Numerical 0 probability for all classes with observation 12639Numerical 0 probability for all classes with observation 12645Numerical 0 probability for all classes with observation 12649Numerical 0 probability for all classes with observation 12764Numerical 0 probability for all classes with observation 12853Numerical 0 probability for all classes with observation 12875Numerical 0 probability for all classes with observation 12902Numerical 0 probability for all classes with observation 13051Numerical 0 probability for all classes with observation 13142Numerical 0 probability for all classes with observation 13349Numerical 0 probability for all classes with observation 13359Numerical 0 probability for all classes with observation 13484Numerical 0 probability for all classes with observation 13642Numerical 0 probability for all classes with observation 13665Numerical 0 probability for all classes with observation 13745Numerical 0 probability for all classes with observation 13749Numerical 0 probability for all classes with observation 14267Numerical 0 probability for all classes with observation 14270Numerical 0 probability for all classes with observation 14496Numerical 0 probability for all classes with observation 14777Numerical 0 probability for all classes with observation 14842Numerical 0 probability for all classes with observation 15011Numerical 0 probability for all classes with observation 15051Numerical 0 probability for all classes with observation 15175Numerical 0 probability for all classes with observation 15264Numerical 0 probability for all classes with observation 68Numerical 0 probability for all classes with observation 318Numerical 0 probability for all classes with observation 334Numerical 0 probability for all classes with observation 650Numerical 0 probability for all classes with observation 669Numerical 0 probability for all classes with observation 749Numerical 0 probability for all classes with observation 760Numerical 0 probability for all classes with observation 777Numerical 0 probability for all classes with observation 914Numerical 0 probability for all classes with observation 1098Numerical 0 probability for all classes with observation 1404Numerical 0 probability for all classes with observation 1466Numerical 0 probability for all classes with observation 1494Numerical 0 probability for all classes with observation 1620Numerical 0 probability for all classes with observation 1732Numerical 0 probability for all classes with observation 1772Numerical 0 probability for all classes with observation 2002Numerical 0 probability for all classes with observation 2044Numerical 0 probability for all classes with observation 2248Numerical 0 probability for all classes with observation 2453Numerical 0 probability for all classes with observation 2882Numerical 0 probability for all classes with observation 3059Numerical 0 probability for all classes with observation 3126Numerical 0 probability for all classes with observation 3180Numerical 0 probability for all classes with observation 3265Numerical 0 probability for all classes with observation 3548Numerical 0 probability for all classes with observation 3786Numerical 0 probability for all classes with observation 4040Numerical 0 probability for all classes with observation 4103Numerical 0 probability for all classes with observation 4259Numerical 0 probability for all classes with observation 4313Numerical 0 probability for all classes with observation 4434Numerical 0 probability for all classes with observation 4613Numerical 0 probability for all classes with observation 4669Numerical 0 probability for all classes with observation 4869Numerical 0 probability for all classes with observation 4903Numerical 0 probability for all classes with observation 5321Numerical 0 probability for all classes with observation 5326Numerical 0 probability for all classes with observation 5379Numerical 0 probability for all classes with observation 5425Numerical 0 probability for all classes with observation 5461Numerical 0 probability for all classes with observation 5719Numerical 0 probability for all classes with observation 5736Numerical 0 probability for all classes with observation 6041Numerical 0 probability for all classes with observation 6145Numerical 0 probability for all classes with observation 6196Numerical 0 probability for all classes with observation 6342Numerical 0 probability for all classes with observation 6541Numerical 0 probability for all classes with observation 6595Numerical 0 probability for all classes with observation 6612Numerical 0 probability for all classes with observation 6810Numerical 0 probability for all classes with observation 7055Numerical 0 probability for all classes with observation 7165Numerical 0 probability for all classes with observation 7445Numerical 0 probability for all classes with observation 7566Numerical 0 probability for all classes with observation 7668Numerical 0 probability for all classes with observation 7887Numerical 0 probability for all classes with observation 7949Numerical 0 probability for all classes with observation 7970Numerical 0 probability for all classes with observation 8085Numerical 0 probability for all classes with observation 8110Numerical 0 probability for all classes with observation 8111Numerical 0 probability for all classes with observation 8128Numerical 0 probability for all classes with observation 8163Numerical 0 probability for all classes with observation 8428Numerical 0 probability for all classes with observation 8636Numerical 0 probability for all classes with observation 8663Numerical 0 probability for all classes with observation 8882Numerical 0 probability for all classes with observation 8907Numerical 0 probability for all classes with observation 9080Numerical 0 probability for all classes with observation 9183Numerical 0 probability for all classes with observation 9625Numerical 0 probability for all classes with observation 9684Numerical 0 probability for all classes with observation 9725Numerical 0 probability for all classes with observation 9805Numerical 0 probability for all classes with observation 9809Numerical 0 probability for all classes with observation 9824Numerical 0 probability for all classes with observation 9883Numerical 0 probability for all classes with observation 9949Numerical 0 probability for all classes with observation 10072Numerical 0 probability for all classes with observation 10122Numerical 0 probability for all classes with observation 10311Numerical 0 probability for all classes with observation 10351Numerical 0 probability for all classes with observation 10373Numerical 0 probability for all classes with observation 10384Numerical 0 probability for all classes with observation 10598Numerical 0 probability for all classes with observation 10609Numerical 0 probability for all classes with observation 10633Numerical 0 probability for all classes with observation 10677Numerical 0 probability for all classes with observation 10981Numerical 0 probability for all classes with observation 11071Numerical 0 probability for all classes with observation 11188Numerical 0 probability for all classes with observation 11225Numerical 0 probability for all classes with observation 11636Numerical 0 probability for all classes with observation 11657Numerical 0 probability for all classes with observation 11751Numerical 0 probability for all classes with observation 11859Numerical 0 probability for all classes with observation 12254Numerical 0 probability for all classes with observation 12275Numerical 0 probability for all classes with observation 12333Numerical 0 probability for all classes with observation 12595Numerical 0 probability for all classes with observation 12889Numerical 0 probability for all classes with observation 13023Numerical 0 probability for all classes with observation 13136Numerical 0 probability for all classes with observation 13228Numerical 0 probability for all classes with observation 13346Numerical 0 probability for all classes with observation 13504Numerical 0 probability for all classes with observation 13513Numerical 0 probability for all classes with observation 13555Numerical 0 probability for all classes with observation 13576Numerical 0 probability for all classes with observation 13609Numerical 0 probability for all classes with observation 13752Numerical 0 probability for all classes with observation 13824Numerical 0 probability for all classes with observation 13837Numerical 0 probability for all classes with observation 14252Numerical 0 probability for all classes with observation 14316Numerical 0 probability for all classes with observation 14553Numerical 0 probability for all classes with observation 14613Numerical 0 probability for all classes with observation 14675Numerical 0 probability for all classes with observation 14678Numerical 0 probability for all classes with observation 14686Numerical 0 probability for all classes with observation 14824Numerical 0 probability for all classes with observation 14893Numerical 0 probability for all classes with observation 14995Numerical 0 probability for all classes with observation 15090Numerical 0 probability for all classes with observation 15154Numerical 0 probability for all classes with observation 424Numerical 0 probability for all classes with observation 539Numerical 0 probability for all classes with observation 590Numerical 0 probability for all classes with observation 747Numerical 0 probability for all classes with observation 775Numerical 0 probability for all classes with observation 1070Numerical 0 probability for all classes with observation 1140Numerical 0 probability for all classes with observation 1406Numerical 0 probability for all classes with observation 1477Numerical 0 probability for all classes with observation 1503Numerical 0 probability for all classes with observation 1685Numerical 0 probability for all classes with observation 1817Numerical 0 probability for all classes with observation 1870Numerical 0 probability for all classes with observation 1919Numerical 0 probability for all classes with observation 1972Numerical 0 probability for all classes with observation 2015Numerical 0 probability for all classes with observation 2077Numerical 0 probability for all classes with observation 2349Numerical 0 probability for all classes with observation 2351Numerical 0 probability for all classes with observation 2479Numerical 0 probability for all classes with observation 2530Numerical 0 probability for all classes with observation 2695Numerical 0 probability for all classes with observation 2702Numerical 0 probability for all classes with observation 2924Numerical 0 probability for all classes with observation 3254Numerical 0 probability for all classes with observation 3434Numerical 0 probability for all classes with observation 3462Numerical 0 probability for all classes with observation 3502Numerical 0 probability for all classes with observation 3531Numerical 0 probability for all classes with observation 3564Numerical 0 probability for all classes with observation 3622Numerical 0 probability for all classes with observation 3686Numerical 0 probability for all classes with observation 4078Numerical 0 probability for all classes with observation 4207Numerical 0 probability for all classes with observation 4584Numerical 0 probability for all classes with observation 4903Numerical 0 probability for all classes with observation 5047Numerical 0 probability for all classes with observation 5197Numerical 0 probability for all classes with observation 5311Numerical 0 probability for all classes with observation 5510Numerical 0 probability for all classes with observation 5650Numerical 0 probability for all classes with observation 6009Numerical 0 probability for all classes with observation 6381Numerical 0 probability for all classes with observation 6567Numerical 0 probability for all classes with observation 6878Numerical 0 probability for all classes with observation 6916Numerical 0 probability for all classes with observation 7055Numerical 0 probability for all classes with observation 7227Numerical 0 probability for all classes with observation 7239Numerical 0 probability for all classes with observation 7309Numerical 0 probability for all classes with observation 7381Numerical 0 probability for all classes with observation 7434Numerical 0 probability for all classes with observation 7471Numerical 0 probability for all classes with observation 7553Numerical 0 probability for all classes with observation 7604Numerical 0 probability for all classes with observation 7667Numerical 0 probability for all classes with observation 7674Numerical 0 probability for all classes with observation 7780Numerical 0 probability for all classes with observation 8304Numerical 0 probability for all classes with observation 8329Numerical 0 probability for all classes with observation 8381Numerical 0 probability for all classes with observation 8460Numerical 0 probability for all classes with observation 8509Numerical 0 probability for all classes with observation 8838Numerical 0 probability for all classes with observation 8973Numerical 0 probability for all classes with observation 9007Numerical 0 probability for all classes with observation 9143Numerical 0 probability for all classes with observation 9443Numerical 0 probability for all classes with observation 9536Numerical 0 probability for all classes with observation 9560Numerical 0 probability for all classes with observation 9577Numerical 0 probability for all classes with observation 9981Numerical 0 probability for all classes with observation 10092Numerical 0 probability for all classes with observation 10255Numerical 0 probability for all classes with observation 10316Numerical 0 probability for all classes with observation 10478Numerical 0 probability for all classes with observation 10726Numerical 0 probability for all classes with observation 11063Numerical 0 probability for all classes with observation 11124Numerical 0 probability for all classes with observation 11129Numerical 0 probability for all classes with observation 11376Numerical 0 probability for all classes with observation 11465Numerical 0 probability for all classes with observation 11515Numerical 0 probability for all classes with observation 11674Numerical 0 probability for all classes with observation 11678Numerical 0 probability for all classes with observation 11881Numerical 0 probability for all classes with observation 11915Numerical 0 probability for all classes with observation 11984Numerical 0 probability for all classes with observation 12155Numerical 0 probability for all classes with observation 12344Numerical 0 probability for all classes with observation 12431Numerical 0 probability for all classes with observation 12518Numerical 0 probability for all classes with observation 12792Numerical 0 probability for all classes with observation 12854Numerical 0 probability for all classes with observation 12883Numerical 0 probability for all classes with observation 12909Numerical 0 probability for all classes with observation 13118Numerical 0 probability for all classes with observation 13188Numerical 0 probability for all classes with observation 13414Numerical 0 probability for all classes with observation 13419Numerical 0 probability for all classes with observation 13501Numerical 0 probability for all classes with observation 13585Numerical 0 probability for all classes with observation 13815Numerical 0 probability for all classes with observation 13913Numerical 0 probability for all classes with observation 14361Numerical 0 probability for all classes with observation 14423Numerical 0 probability for all classes with observation 14503Numerical 0 probability for all classes with observation 15041Numerical 0 probability for all classes with observation 15126Numerical 0 probability for all classes with observation 12Numerical 0 probability for all classes with observation 292Numerical 0 probability for all classes with observation 511Numerical 0 probability for all classes with observation 518Numerical 0 probability for all classes with observation 648Numerical 0 probability for all classes with observation 695Numerical 0 probability for all classes with observation 777Numerical 0 probability for all classes with observation 797Numerical 0 probability for all classes with observation 1156Numerical 0 probability for all classes with observation 1212Numerical 0 probability for all classes with observation 1224Numerical 0 probability for all classes with observation 1227Numerical 0 probability for all classes with observation 1280Numerical 0 probability for all classes with observation 1500Numerical 0 probability for all classes with observation 1587Numerical 0 probability for all classes with observation 1598Numerical 0 probability for all classes with observation 1961Numerical 0 probability for all classes with observation 2284Numerical 0 probability for all classes with observation 2286Numerical 0 probability for all classes with observation 2292Numerical 0 probability for all classes with observation 2475Numerical 0 probability for all classes with observation 2725Numerical 0 probability for all classes with observation 2863Numerical 0 probability for all classes with observation 2888Numerical 0 probability for all classes with observation 3201Numerical 0 probability for all classes with observation 3325Numerical 0 probability for all classes with observation 3338Numerical 0 probability for all classes with observation 3575Numerical 0 probability for all classes with observation 3802Numerical 0 probability for all classes with observation 3948Numerical 0 probability for all classes with observation 3963Numerical 0 probability for all classes with observation 4076Numerical 0 probability for all classes with observation 4081Numerical 0 probability for all classes with observation 4163Numerical 0 probability for all classes with observation 4249Numerical 0 probability for all classes with observation 4327Numerical 0 probability for all classes with observation 4381Numerical 0 probability for all classes with observation 4515Numerical 0 probability for all classes with observation 4753Numerical 0 probability for all classes with observation 4797Numerical 0 probability for all classes with observation 5174Numerical 0 probability for all classes with observation 5285Numerical 0 probability for all classes with observation 5386Numerical 0 probability for all classes with observation 5460Numerical 0 probability for all classes with observation 5681Numerical 0 probability for all classes with observation 5715Numerical 0 probability for all classes with observation 5724Numerical 0 probability for all classes with observation 5766Numerical 0 probability for all classes with observation 5775Numerical 0 probability for all classes with observation 5983Numerical 0 probability for all classes with observation 5996Numerical 0 probability for all classes with observation 6266Numerical 0 probability for all classes with observation 6335Numerical 0 probability for all classes with observation 6392Numerical 0 probability for all classes with observation 6598Numerical 0 probability for all classes with observation 6663Numerical 0 probability for all classes with observation 6688Numerical 0 probability for all classes with observation 6979Numerical 0 probability for all classes with observation 7156Numerical 0 probability for all classes with observation 7238Numerical 0 probability for all classes with observation 7262Numerical 0 probability for all classes with observation 7339Numerical 0 probability for all classes with observation 7351Numerical 0 probability for all classes with observation 7357Numerical 0 probability for all classes with observation 7538Numerical 0 probability for all classes with observation 7568Numerical 0 probability for all classes with observation 7618Numerical 0 probability for all classes with observation 7905Numerical 0 probability for all classes with observation 7911Numerical 0 probability for all classes with observation 8082Numerical 0 probability for all classes with observation 8108Numerical 0 probability for all classes with observation 8139Numerical 0 probability for all classes with observation 8152Numerical 0 probability for all classes with observation 8441Numerical 0 probability for all classes with observation 8674Numerical 0 probability for all classes with observation 9354Numerical 0 probability for all classes with observation 9544Numerical 0 probability for all classes with observation 9546Numerical 0 probability for all classes with observation 9590Numerical 0 probability for all classes with observation 9663Numerical 0 probability for all classes with observation 9798Numerical 0 probability for all classes with observation 10200Numerical 0 probability for all classes with observation 10357Numerical 0 probability for all classes with observation 11012Numerical 0 probability for all classes with observation 11041Numerical 0 probability for all classes with observation 11055Numerical 0 probability for all classes with observation 11074Numerical 0 probability for all classes with observation 11174Numerical 0 probability for all classes with observation 11177Numerical 0 probability for all classes with observation 11198Numerical 0 probability for all classes with observation 11225Numerical 0 probability for all classes with observation 11311Numerical 0 probability for all classes with observation 11324Numerical 0 probability for all classes with observation 11502Numerical 0 probability for all classes with observation 11521Numerical 0 probability for all classes with observation 11682Numerical 0 probability for all classes with observation 11820Numerical 0 probability for all classes with observation 11929Numerical 0 probability for all classes with observation 12130Numerical 0 probability for all classes with observation 12824Numerical 0 probability for all classes with observation 12920Numerical 0 probability for all classes with observation 13163Numerical 0 probability for all classes with observation 13169Numerical 0 probability for all classes with observation 13344Numerical 0 probability for all classes with observation 13362Numerical 0 probability for all classes with observation 13397Numerical 0 probability for all classes with observation 13423Numerical 0 probability for all classes with observation 13439Numerical 0 probability for all classes with observation 13476Numerical 0 probability for all classes with observation 13490Numerical 0 probability for all classes with observation 13496Numerical 0 probability for all classes with observation 13587Numerical 0 probability for all classes with observation 13595Numerical 0 probability for all classes with observation 13807Numerical 0 probability for all classes with observation 13901Numerical 0 probability for all classes with observation 13943Numerical 0 probability for all classes with observation 13994Numerical 0 probability for all classes with observation 14063Numerical 0 probability for all classes with observation 14107Numerical 0 probability for all classes with observation 14140Numerical 0 probability for all classes with observation 14182Numerical 0 probability for all classes with observation 14223Numerical 0 probability for all classes with observation 14523Numerical 0 probability for all classes with observation 14554Numerical 0 probability for all classes with observation 14647Numerical 0 probability for all classes with observation 14652Numerical 0 probability for all classes with observation 14696Numerical 0 probability for all classes with observation 14743Numerical 0 probability for all classes with observation 14771Numerical 0 probability for all classes with observation 14908Numerical 0 probability for all classes with observation 15191Numerical 0 probability for all classes with observation 185Numerical 0 probability for all classes with observation 351Numerical 0 probability for all classes with observation 702Numerical 0 probability for all classes with observation 794Numerical 0 probability for all classes with observation 802Numerical 0 probability for all classes with observation 991Numerical 0 probability for all classes with observation 1080Numerical 0 probability for all classes with observation 1081Numerical 0 probability for all classes with observation 1093Numerical 0 probability for all classes with observation 1303Numerical 0 probability for all classes with observation 1330Numerical 0 probability for all classes with observation 1400Numerical 0 probability for all classes with observation 1438Numerical 0 probability for all classes with observation 1494Numerical 0 probability for all classes with observation 2091Numerical 0 probability for all classes with observation 2265Numerical 0 probability for all classes with observation 2315Numerical 0 probability for all classes with observation 2328Numerical 0 probability for all classes with observation 2393Numerical 0 probability for all classes with observation 2753Numerical 0 probability for all classes with observation 2782Numerical 0 probability for all classes with observation 2861Numerical 0 probability for all classes with observation 3006Numerical 0 probability for all classes with observation 3322Numerical 0 probability for all classes with observation 3440Numerical 0 probability for all classes with observation 3559Numerical 0 probability for all classes with observation 3717Numerical 0 probability for all classes with observation 3871Numerical 0 probability for all classes with observation 3963Numerical 0 probability for all classes with observation 3993Numerical 0 probability for all classes with observation 4037Numerical 0 probability for all classes with observation 4164Numerical 0 probability for all classes with observation 4321Numerical 0 probability for all classes with observation 4473Numerical 0 probability for all classes with observation 4549Numerical 0 probability for all classes with observation 4780Numerical 0 probability for all classes with observation 4932Numerical 0 probability for all classes with observation 4942Numerical 0 probability for all classes with observation 4975Numerical 0 probability for all classes with observation 5079Numerical 0 probability for all classes with observation 5100Numerical 0 probability for all classes with observation 5155Numerical 0 probability for all classes with observation 5232Numerical 0 probability for all classes with observation 5309Numerical 0 probability for all classes with observation 5370Numerical 0 probability for all classes with observation 5646Numerical 0 probability for all classes with observation 5702Numerical 0 probability for all classes with observation 5886Numerical 0 probability for all classes with observation 5998Numerical 0 probability for all classes with observation 6108Numerical 0 probability for all classes with observation 6214Numerical 0 probability for all classes with observation 6255Numerical 0 probability for all classes with observation 6349Numerical 0 probability for all classes with observation 6363Numerical 0 probability for all classes with observation 6365Numerical 0 probability for all classes with observation 6584Numerical 0 probability for all classes with observation 6745Numerical 0 probability for all classes with observation 6756Numerical 0 probability for all classes with observation 6825Numerical 0 probability for all classes with observation 6849Numerical 0 probability for all classes with observation 6927Numerical 0 probability for all classes with observation 7089Numerical 0 probability for all classes with observation 7290Numerical 0 probability for all classes with observation 7333Numerical 0 probability for all classes with observation 7476Numerical 0 probability for all classes with observation 7541Numerical 0 probability for all classes with observation 7555Numerical 0 probability for all classes with observation 7667Numerical 0 probability for all classes with observation 7721Numerical 0 probability for all classes with observation 7864Numerical 0 probability for all classes with observation 8221Numerical 0 probability for all classes with observation 8276Numerical 0 probability for all classes with observation 8372Numerical 0 probability for all classes with observation 8697Numerical 0 probability for all classes with observation 8712Numerical 0 probability for all classes with observation 8745Numerical 0 probability for all classes with observation 8868Numerical 0 probability for all classes with observation 8896Numerical 0 probability for all classes with observation 9250Numerical 0 probability for all classes with observation 9524Numerical 0 probability for all classes with observation 9601Numerical 0 probability for all classes with observation 9998Numerical 0 probability for all classes with observation 10359Numerical 0 probability for all classes with observation 10410Numerical 0 probability for all classes with observation 10543Numerical 0 probability for all classes with observation 10573Numerical 0 probability for all classes with observation 10581Numerical 0 probability for all classes with observation 10666Numerical 0 probability for all classes with observation 10754Numerical 0 probability for all classes with observation 10908Numerical 0 probability for all classes with observation 10950Numerical 0 probability for all classes with observation 10973Numerical 0 probability for all classes with observation 11460Numerical 0 probability for all classes with observation 11486Numerical 0 probability for all classes with observation 11892Numerical 0 probability for all classes with observation 12038Numerical 0 probability for all classes with observation 12160Numerical 0 probability for all classes with observation 12259Numerical 0 probability for all classes with observation 12299Numerical 0 probability for all classes with observation 12352Numerical 0 probability for all classes with observation 12431Numerical 0 probability for all classes with observation 12456Numerical 0 probability for all classes with observation 12785Numerical 0 probability for all classes with observation 12802Numerical 0 probability for all classes with observation 12875Numerical 0 probability for all classes with observation 12876Numerical 0 probability for all classes with observation 12896Numerical 0 probability for all classes with observation 13124Numerical 0 probability for all classes with observation 13322Numerical 0 probability for all classes with observation 13415Numerical 0 probability for all classes with observation 13438Numerical 0 probability for all classes with observation 13689Numerical 0 probability for all classes with observation 13857Numerical 0 probability for all classes with observation 13916Numerical 0 probability for all classes with observation 14041Numerical 0 probability for all classes with observation 14348Numerical 0 probability for all classes with observation 14373Numerical 0 probability for all classes with observation 14378Numerical 0 probability for all classes with observation 14422Numerical 0 probability for all classes with observation 14615Numerical 0 probability for all classes with observation 14635Numerical 0 probability for all classes with observation 14722Numerical 0 probability for all classes with observation 14972Numerical 0 probability for all classes with observation 15064Numerical 0 probability for all classes with observation 9045Numerical 0 probability for all classes with observation 10088Numerical 0 probability for all classes with observation 129Numerical 0 probability for all classes with observation 187Numerical 0 probability for all classes with observation 380Numerical 0 probability for all classes with observation 465Numerical 0 probability for all classes with observation 553Numerical 0 probability for all classes with observation 711Numerical 0 probability for all classes with observation 914Numerical 0 probability for all classes with observation 1096Numerical 0 probability for all classes with observation 1133Numerical 0 probability for all classes with observation 1229Numerical 0 probability for all classes with observation 1311Numerical 0 probability for all classes with observation 1455Numerical 0 probability for all classes with observation 1464Numerical 0 probability for all classes with observation 1800Numerical 0 probability for all classes with observation 2137Numerical 0 probability for all classes with observation 2156Numerical 0 probability for all classes with observation 2228Numerical 0 probability for all classes with observation 2254Numerical 0 probability for all classes with observation 2271Numerical 0 probability for all classes with observation 2286Numerical 0 probability for all classes with observation 2355Numerical 0 probability for all classes with observation 2368Numerical 0 probability for all classes with observation 2686Numerical 0 probability for all classes with observation 2810Numerical 0 probability for all classes with observation 3337Numerical 0 probability for all classes with observation 3433Numerical 0 probability for all classes with observation 3451Numerical 0 probability for all classes with observation 3458Numerical 0 probability for all classes with observation 3482Numerical 0 probability for all classes with observation 3731Numerical 0 probability for all classes with observation 3813Numerical 0 probability for all classes with observation 3838Numerical 0 probability for all classes with observation 3896Numerical 0 probability for all classes with observation 4029Numerical 0 probability for all classes with observation 4131Numerical 0 probability for all classes with observation 4489Numerical 0 probability for all classes with observation 4783Numerical 0 probability for all classes with observation 5047Numerical 0 probability for all classes with observation 5063Numerical 0 probability for all classes with observation 5230Numerical 0 probability for all classes with observation 5337Numerical 0 probability for all classes with observation 5442Numerical 0 probability for all classes with observation 5465Numerical 0 probability for all classes with observation 6022Numerical 0 probability for all classes with observation 6303Numerical 0 probability for all classes with observation 6369Numerical 0 probability for all classes with observation 6569Numerical 0 probability for all classes with observation 6918Numerical 0 probability for all classes with observation 7139Numerical 0 probability for all classes with observation 7218Numerical 0 probability for all classes with observation 7226Numerical 0 probability for all classes with observation 7569Numerical 0 probability for all classes with observation 7604Numerical 0 probability for all classes with observation 7642Numerical 0 probability for all classes with observation 7761Numerical 0 probability for all classes with observation 7852Numerical 0 probability for all classes with observation 7876Numerical 0 probability for all classes with observation 7940Numerical 0 probability for all classes with observation 8276Numerical 0 probability for all classes with observation 8288Numerical 0 probability for all classes with observation 8341Numerical 0 probability for all classes with observation 8408Numerical 0 probability for all classes with observation 8418Numerical 0 probability for all classes with observation 8525Numerical 0 probability for all classes with observation 8648Numerical 0 probability for all classes with observation 8700Numerical 0 probability for all classes with observation 8785Numerical 0 probability for all classes with observation 8862Numerical 0 probability for all classes with observation 8879Numerical 0 probability for all classes with observation 9045Numerical 0 probability for all classes with observation 9126Numerical 0 probability for all classes with observation 9205Numerical 0 probability for all classes with observation 9361Numerical 0 probability for all classes with observation 9365Numerical 0 probability for all classes with observation 9427Numerical 0 probability for all classes with observation 9776Numerical 0 probability for all classes with observation 10003Numerical 0 probability for all classes with observation 10088Numerical 0 probability for all classes with observation 10185Numerical 0 probability for all classes with observation 10191Numerical 0 probability for all classes with observation 10604Numerical 0 probability for all classes with observation 10685Numerical 0 probability for all classes with observation 10730Numerical 0 probability for all classes with observation 10775Numerical 0 probability for all classes with observation 10926Numerical 0 probability for all classes with observation 11091Numerical 0 probability for all classes with observation 11387Numerical 0 probability for all classes with observation 11478Numerical 0 probability for all classes with observation 11567Numerical 0 probability for all classes with observation 11700Numerical 0 probability for all classes with observation 11899Numerical 0 probability for all classes with observation 11940Numerical 0 probability for all classes with observation 12054Numerical 0 probability for all classes with observation 12201Numerical 0 probability for all classes with observation 12303Numerical 0 probability for all classes with observation 12386Numerical 0 probability for all classes with observation 12408Numerical 0 probability for all classes with observation 12536Numerical 0 probability for all classes with observation 12949Numerical 0 probability for all classes with observation 13235Numerical 0 probability for all classes with observation 13293Numerical 0 probability for all classes with observation 13638Numerical 0 probability for all classes with observation 14065Numerical 0 probability for all classes with observation 14221Numerical 0 probability for all classes with observation 14325Numerical 0 probability for all classes with observation 14426Numerical 0 probability for all classes with observation 14454Numerical 0 probability for all classes with observation 14490Numerical 0 probability for all classes with observation 14655Numerical 0 probability for all classes with observation 14683Numerical 0 probability for all classes with observation 14740Numerical 0 probability for all classes with observation 14934Numerical 0 probability for all classes with observation 15255Numerical 0 probability for all classes with observation 3296Numerical 0 probability for all classes with observation 5Numerical 0 probability for all classes with observation 33Numerical 0 probability for all classes with observation 99Numerical 0 probability for all classes with observation 239Numerical 0 probability for all classes with observation 364Numerical 0 probability for all classes with observation 742Numerical 0 probability for all classes with observation 746Numerical 0 probability for all classes with observation 792Numerical 0 probability for all classes with observation 793Numerical 0 probability for all classes with observation 927Numerical 0 probability for all classes with observation 991Numerical 0 probability for all classes with observation 1116Numerical 0 probability for all classes with observation 1144Numerical 0 probability for all classes with observation 1277Numerical 0 probability for all classes with observation 1457Numerical 0 probability for all classes with observation 1641Numerical 0 probability for all classes with observation 1683Numerical 0 probability for all classes with observation 1775Numerical 0 probability for all classes with observation 1841Numerical 0 probability for all classes with observation 1881Numerical 0 probability for all classes with observation 1894Numerical 0 probability for all classes with observation 1911Numerical 0 probability for all classes with observation 2065Numerical 0 probability for all classes with observation 2092Numerical 0 probability for all classes with observation 2211Numerical 0 probability for all classes with observation 2319Numerical 0 probability for all classes with observation 2353Numerical 0 probability for all classes with observation 2455Numerical 0 probability for all classes with observation 2612Numerical 0 probability for all classes with observation 2675Numerical 0 probability for all classes with observation 2719Numerical 0 probability for all classes with observation 2728Numerical 0 probability for all classes with observation 3006Numerical 0 probability for all classes with observation 3067Numerical 0 probability for all classes with observation 3152Numerical 0 probability for all classes with observation 3194Numerical 0 probability for all classes with observation 3296Numerical 0 probability for all classes with observation 3395Numerical 0 probability for all classes with observation 3502Numerical 0 probability for all classes with observation 3524Numerical 0 probability for all classes with observation 3545Numerical 0 probability for all classes with observation 3548Numerical 0 probability for all classes with observation 3566Numerical 0 probability for all classes with observation 3867Numerical 0 probability for all classes with observation 4050Numerical 0 probability for all classes with observation 4054Numerical 0 probability for all classes with observation 4195Numerical 0 probability for all classes with observation 4263Numerical 0 probability for all classes with observation 4365Numerical 0 probability for all classes with observation 4508Numerical 0 probability for all classes with observation 4542Numerical 0 probability for all classes with observation 4569Numerical 0 probability for all classes with observation 4589Numerical 0 probability for all classes with observation 4817Numerical 0 probability for all classes with observation 5172Numerical 0 probability for all classes with observation 5385Numerical 0 probability for all classes with observation 5639Numerical 0 probability for all classes with observation 5851Numerical 0 probability for all classes with observation 5920Numerical 0 probability for all classes with observation 6036Numerical 0 probability for all classes with observation 6186Numerical 0 probability for all classes with observation 6233Numerical 0 probability for all classes with observation 6567Numerical 0 probability for all classes with observation 6598Numerical 0 probability for all classes with observation 6625Numerical 0 probability for all classes with observation 7016Numerical 0 probability for all classes with observation 7037Numerical 0 probability for all classes with observation 7343Numerical 0 probability for all classes with observation 7392Numerical 0 probability for all classes with observation 7412Numerical 0 probability for all classes with observation 7520Numerical 0 probability for all classes with observation 7698Numerical 0 probability for all classes with observation 7750Numerical 0 probability for all classes with observation 7866Numerical 0 probability for all classes with observation 8188Numerical 0 probability for all classes with observation 8211Numerical 0 probability for all classes with observation 8336Numerical 0 probability for all classes with observation 8415Numerical 0 probability for all classes with observation 8631Numerical 0 probability for all classes with observation 8662Numerical 0 probability for all classes with observation 8801Numerical 0 probability for all classes with observation 8837Numerical 0 probability for all classes with observation 8848Numerical 0 probability for all classes with observation 8895Numerical 0 probability for all classes with observation 8958Numerical 0 probability for all classes with observation 9582Numerical 0 probability for all classes with observation 9660Numerical 0 probability for all classes with observation 9759Numerical 0 probability for all classes with observation 9792Numerical 0 probability for all classes with observation 9845Numerical 0 probability for all classes with observation 10004Numerical 0 probability for all classes with observation 10031Numerical 0 probability for all classes with observation 10068Numerical 0 probability for all classes with observation 10239Numerical 0 probability for all classes with observation 10246Numerical 0 probability for all classes with observation 10376Numerical 0 probability for all classes with observation 10427Numerical 0 probability for all classes with observation 10801Numerical 0 probability for all classes with observation 10855Numerical 0 probability for all classes with observation 10865Numerical 0 probability for all classes with observation 11131Numerical 0 probability for all classes with observation 11242Numerical 0 probability for all classes with observation 11402Numerical 0 probability for all classes with observation 11457Numerical 0 probability for all classes with observation 11465Numerical 0 probability for all classes with observation 11667Numerical 0 probability for all classes with observation 11713Numerical 0 probability for all classes with observation 11954Numerical 0 probability for all classes with observation 11988Numerical 0 probability for all classes with observation 12037Numerical 0 probability for all classes with observation 12125Numerical 0 probability for all classes with observation 12130Numerical 0 probability for all classes with observation 12193Numerical 0 probability for all classes with observation 12195Numerical 0 probability for all classes with observation 12230Numerical 0 probability for all classes with observation 12321Numerical 0 probability for all classes with observation 12525Numerical 0 probability for all classes with observation 12628Numerical 0 probability for all classes with observation 12724Numerical 0 probability for all classes with observation 12815Numerical 0 probability for all classes with observation 12860Numerical 0 probability for all classes with observation 12960Numerical 0 probability for all classes with observation 13224Numerical 0 probability for all classes with observation 13227Numerical 0 probability for all classes with observation 13249Numerical 0 probability for all classes with observation 13270Numerical 0 probability for all classes with observation 13695Numerical 0 probability for all classes with observation 13700Numerical 0 probability for all classes with observation 13714Numerical 0 probability for all classes with observation 13743Numerical 0 probability for all classes with observation 14153Numerical 0 probability for all classes with observation 14186Numerical 0 probability for all classes with observation 14341Numerical 0 probability for all classes with observation 14400Numerical 0 probability for all classes with observation 14548Numerical 0 probability for all classes with observation 14602Numerical 0 probability for all classes with observation 15006Numerical 0 probability for all classes with observation 15083Numerical 0 probability for all classes with observation 15155Numerical 0 probability for all classes with observation 11Numerical 0 probability for all classes with observation 43Numerical 0 probability for all classes with observation 131Numerical 0 probability for all classes with observation 209Numerical 0 probability for all classes with observation 287Numerical 0 probability for all classes with observation 692Numerical 0 probability for all classes with observation 701Numerical 0 probability for all classes with observation 994Numerical 0 probability for all classes with observation 1100Numerical 0 probability for all classes with observation 1422Numerical 0 probability for all classes with observation 1549Numerical 0 probability for all classes with observation 1551Numerical 0 probability for all classes with observation 1650Numerical 0 probability for all classes with observation 1859Numerical 0 probability for all classes with observation 2038Numerical 0 probability for all classes with observation 2040Numerical 0 probability for all classes with observation 2193Numerical 0 probability for all classes with observation 2423Numerical 0 probability for all classes with observation 2823Numerical 0 probability for all classes with observation 3020Numerical 0 probability for all classes with observation 3086Numerical 0 probability for all classes with observation 3095Numerical 0 probability for all classes with observation 3351Numerical 0 probability for all classes with observation 3559Numerical 0 probability for all classes with observation 3676Numerical 0 probability for all classes with observation 3802Numerical 0 probability for all classes with observation 3809Numerical 0 probability for all classes with observation 4062Numerical 0 probability for all classes with observation 4144Numerical 0 probability for all classes with observation 4174Numerical 0 probability for all classes with observation 4274Numerical 0 probability for all classes with observation 4318Numerical 0 probability for all classes with observation 4354Numerical 0 probability for all classes with observation 4366Numerical 0 probability for all classes with observation 4476Numerical 0 probability for all classes with observation 4724Numerical 0 probability for all classes with observation 4842Numerical 0 probability for all classes with observation 4874Numerical 0 probability for all classes with observation 5062Numerical 0 probability for all classes with observation 5132Numerical 0 probability for all classes with observation 5213Numerical 0 probability for all classes with observation 5452Numerical 0 probability for all classes with observation 5535Numerical 0 probability for all classes with observation 5543Numerical 0 probability for all classes with observation 5724Numerical 0 probability for all classes with observation 5740Numerical 0 probability for all classes with observation 5806Numerical 0 probability for all classes with observation 5858Numerical 0 probability for all classes with observation 5862Numerical 0 probability for all classes with observation 5905Numerical 0 probability for all classes with observation 5916Numerical 0 probability for all classes with observation 6025Numerical 0 probability for all classes with observation 6032Numerical 0 probability for all classes with observation 6067Numerical 0 probability for all classes with observation 6423Numerical 0 probability for all classes with observation 6441Numerical 0 probability for all classes with observation 6588Numerical 0 probability for all classes with observation 6762Numerical 0 probability for all classes with observation 6885Numerical 0 probability for all classes with observation 6906Numerical 0 probability for all classes with observation 6928Numerical 0 probability for all classes with observation 6931Numerical 0 probability for all classes with observation 7008Numerical 0 probability for all classes with observation 7190Numerical 0 probability for all classes with observation 7348Numerical 0 probability for all classes with observation 7575Numerical 0 probability for all classes with observation 7585Numerical 0 probability for all classes with observation 7631Numerical 0 probability for all classes with observation 7651Numerical 0 probability for all classes with observation 7654Numerical 0 probability for all classes with observation 7717Numerical 0 probability for all classes with observation 7719Numerical 0 probability for all classes with observation 7810Numerical 0 probability for all classes with observation 7841Numerical 0 probability for all classes with observation 8274Numerical 0 probability for all classes with observation 8326Numerical 0 probability for all classes with observation 8518Numerical 0 probability for all classes with observation 8576Numerical 0 probability for all classes with observation 8666Numerical 0 probability for all classes with observation 8740Numerical 0 probability for all classes with observation 8822Numerical 0 probability for all classes with observation 9068Numerical 0 probability for all classes with observation 9232Numerical 0 probability for all classes with observation 9256Numerical 0 probability for all classes with observation 9259Numerical 0 probability for all classes with observation 9279Numerical 0 probability for all classes with observation 9321Numerical 0 probability for all classes with observation 9433Numerical 0 probability for all classes with observation 9681Numerical 0 probability for all classes with observation 9698Numerical 0 probability for all classes with observation 9938Numerical 0 probability for all classes with observation 10064Numerical 0 probability for all classes with observation 10164Numerical 0 probability for all classes with observation 10494Numerical 0 probability for all classes with observation 10502Numerical 0 probability for all classes with observation 10627Numerical 0 probability for all classes with observation 10870Numerical 0 probability for all classes with observation 10907Numerical 0 probability for all classes with observation 11093Numerical 0 probability for all classes with observation 11168Numerical 0 probability for all classes with observation 11234Numerical 0 probability for all classes with observation 11271Numerical 0 probability for all classes with observation 11360Numerical 0 probability for all classes with observation 11410Numerical 0 probability for all classes with observation 11433Numerical 0 probability for all classes with observation 11801Numerical 0 probability for all classes with observation 12066Numerical 0 probability for all classes with observation 12317Numerical 0 probability for all classes with observation 12410Numerical 0 probability for all classes with observation 12411Numerical 0 probability for all classes with observation 12472Numerical 0 probability for all classes with observation 12487Numerical 0 probability for all classes with observation 12535Numerical 0 probability for all classes with observation 12575Numerical 0 probability for all classes with observation 12734Numerical 0 probability for all classes with observation 13143Numerical 0 probability for all classes with observation 13340Numerical 0 probability for all classes with observation 13376Numerical 0 probability for all classes with observation 13633Numerical 0 probability for all classes with observation 13639Numerical 0 probability for all classes with observation 13834Numerical 0 probability for all classes with observation 13913Numerical 0 probability for all classes with observation 14045Numerical 0 probability for all classes with observation 14053Numerical 0 probability for all classes with observation 14314Numerical 0 probability for all classes with observation 14509Numerical 0 probability for all classes with observation 14592Numerical 0 probability for all classes with observation 14755Numerical 0 probability for all classes with observation 14762Numerical 0 probability for all classes with observation 14834Numerical 0 probability for all classes with observation 15035Numerical 0 probability for all classes with observation 15158Numerical 0 probability for all classes with observation 15203Numerical 0 probability for all classes with observation 15236Numerical 0 probability for all classes with observation 7124Numerical 0 probability for all classes with observation 11466Numerical 0 probability for all classes with observation 57Numerical 0 probability for all classes with observation 172Numerical 0 probability for all classes with observation 296Numerical 0 probability for all classes with observation 381Numerical 0 probability for all classes with observation 387Numerical 0 probability for all classes with observation 481Numerical 0 probability for all classes with observation 585Numerical 0 probability for all classes with observation 679Numerical 0 probability for all classes with observation 785Numerical 0 probability for all classes with observation 831Numerical 0 probability for all classes with observation 955Numerical 0 probability for all classes with observation 1033Numerical 0 probability for all classes with observation 1264Numerical 0 probability for all classes with observation 1411Numerical 0 probability for all classes with observation 1499Numerical 0 probability for all classes with observation 1514Numerical 0 probability for all classes with observation 1615Numerical 0 probability for all classes with observation 1649Numerical 0 probability for all classes with observation 1687Numerical 0 probability for all classes with observation 1885Numerical 0 probability for all classes with observation 2053Numerical 0 probability for all classes with observation 2112Numerical 0 probability for all classes with observation 2124Numerical 0 probability for all classes with observation 2147Numerical 0 probability for all classes with observation 2190Numerical 0 probability for all classes with observation 2201Numerical 0 probability for all classes with observation 2398Numerical 0 probability for all classes with observation 2446Numerical 0 probability for all classes with observation 2918Numerical 0 probability for all classes with observation 2959Numerical 0 probability for all classes with observation 3070Numerical 0 probability for all classes with observation 3233Numerical 0 probability for all classes with observation 3294Numerical 0 probability for all classes with observation 3520Numerical 0 probability for all classes with observation 3731Numerical 0 probability for all classes with observation 3739Numerical 0 probability for all classes with observation 3815Numerical 0 probability for all classes with observation 3842Numerical 0 probability for all classes with observation 4117Numerical 0 probability for all classes with observation 4122Numerical 0 probability for all classes with observation 4404Numerical 0 probability for all classes with observation 4464Numerical 0 probability for all classes with observation 4528Numerical 0 probability for all classes with observation 4595Numerical 0 probability for all classes with observation 4718Numerical 0 probability for all classes with observation 4781Numerical 0 probability for all classes with observation 4852Numerical 0 probability for all classes with observation 5279Numerical 0 probability for all classes with observation 5305Numerical 0 probability for all classes with observation 5318Numerical 0 probability for all classes with observation 5516Numerical 0 probability for all classes with observation 5804Numerical 0 probability for all classes with observation 5916Numerical 0 probability for all classes with observation 6066Numerical 0 probability for all classes with observation 6087Numerical 0 probability for all classes with observation 6413Numerical 0 probability for all classes with observation 6515Numerical 0 probability for all classes with observation 6627Numerical 0 probability for all classes with observation 6946Numerical 0 probability for all classes with observation 6986Numerical 0 probability for all classes with observation 7124Numerical 0 probability for all classes with observation 7174Numerical 0 probability for all classes with observation 7302Numerical 0 probability for all classes with observation 7529Numerical 0 probability for all classes with observation 7538Numerical 0 probability for all classes with observation 7540Numerical 0 probability for all classes with observation 7579Numerical 0 probability for all classes with observation 7630Numerical 0 probability for all classes with observation 7642Numerical 0 probability for all classes with observation 7668Numerical 0 probability for all classes with observation 7681Numerical 0 probability for all classes with observation 7807Numerical 0 probability for all classes with observation 7851Numerical 0 probability for all classes with observation 7890Numerical 0 probability for all classes with observation 8119Numerical 0 probability for all classes with observation 8263Numerical 0 probability for all classes with observation 8477Numerical 0 probability for all classes with observation 8570Numerical 0 probability for all classes with observation 8669Numerical 0 probability for all classes with observation 8901Numerical 0 probability for all classes with observation 8953Numerical 0 probability for all classes with observation 9124Numerical 0 probability for all classes with observation 9316Numerical 0 probability for all classes with observation 9557Numerical 0 probability for all classes with observation 9734Numerical 0 probability for all classes with observation 9991Numerical 0 probability for all classes with observation 10006Numerical 0 probability for all classes with observation 10116Numerical 0 probability for all classes with observation 10473Numerical 0 probability for all classes with observation 10582Numerical 0 probability for all classes with observation 10587Numerical 0 probability for all classes with observation 10656Numerical 0 probability for all classes with observation 10712Numerical 0 probability for all classes with observation 10873Numerical 0 probability for all classes with observation 10921Numerical 0 probability for all classes with observation 10958Numerical 0 probability for all classes with observation 11315Numerical 0 probability for all classes with observation 11423Numerical 0 probability for all classes with observation 11452Numerical 0 probability for all classes with observation 11466Numerical 0 probability for all classes with observation 11523Numerical 0 probability for all classes with observation 11671Numerical 0 probability for all classes with observation 11800Numerical 0 probability for all classes with observation 11930Numerical 0 probability for all classes with observation 12023Numerical 0 probability for all classes with observation 12132Numerical 0 probability for all classes with observation 12291Numerical 0 probability for all classes with observation 12355Numerical 0 probability for all classes with observation 12496Numerical 0 probability for all classes with observation 12625Numerical 0 probability for all classes with observation 12735Numerical 0 probability for all classes with observation 12983Numerical 0 probability for all classes with observation 13031Numerical 0 probability for all classes with observation 13158Numerical 0 probability for all classes with observation 13234Numerical 0 probability for all classes with observation 13378Numerical 0 probability for all classes with observation 13692Numerical 0 probability for all classes with observation 14053Numerical 0 probability for all classes with observation 14056Numerical 0 probability for all classes with observation 14083Numerical 0 probability for all classes with observation 14189Numerical 0 probability for all classes with observation 14385Numerical 0 probability for all classes with observation 14665Numerical 0 probability for all classes with observation 14695Numerical 0 probability for all classes with observation 14769Numerical 0 probability for all classes with observation 14998Numerical 0 probability for all classes with observation 15076Numerical 0 probability for all classes with observation 15084Numerical 0 probability for all classes with observation 15205Numerical 0 probability for all classes with observation 4742Numerical 0 probability for all classes with observation 166Numerical 0 probability for all classes with observation 293Numerical 0 probability for all classes with observation 364Numerical 0 probability for all classes with observation 493Numerical 0 probability for all classes with observation 595Numerical 0 probability for all classes with observation 660Numerical 0 probability for all classes with observation 664Numerical 0 probability for all classes with observation 863Numerical 0 probability for all classes with observation 865Numerical 0 probability for all classes with observation 960Numerical 0 probability for all classes with observation 1046Numerical 0 probability for all classes with observation 1094Numerical 0 probability for all classes with observation 1126Numerical 0 probability for all classes with observation 1331Numerical 0 probability for all classes with observation 1409Numerical 0 probability for all classes with observation 1680Numerical 0 probability for all classes with observation 1683Numerical 0 probability for all classes with observation 1746Numerical 0 probability for all classes with observation 1786Numerical 0 probability for all classes with observation 1871Numerical 0 probability for all classes with observation 1900Numerical 0 probability for all classes with observation 2281Numerical 0 probability for all classes with observation 2292Numerical 0 probability for all classes with observation 2296Numerical 0 probability for all classes with observation 2326Numerical 0 probability for all classes with observation 2489Numerical 0 probability for all classes with observation 2504Numerical 0 probability for all classes with observation 2517Numerical 0 probability for all classes with observation 2809Numerical 0 probability for all classes with observation 2826Numerical 0 probability for all classes with observation 2893Numerical 0 probability for all classes with observation 3170Numerical 0 probability for all classes with observation 3280Numerical 0 probability for all classes with observation 3379Numerical 0 probability for all classes with observation 3429Numerical 0 probability for all classes with observation 3449Numerical 0 probability for all classes with observation 3494Numerical 0 probability for all classes with observation 3502Numerical 0 probability for all classes with observation 3544Numerical 0 probability for all classes with observation 3721Numerical 0 probability for all classes with observation 3869Numerical 0 probability for all classes with observation 3876Numerical 0 probability for all classes with observation 4173Numerical 0 probability for all classes with observation 4313Numerical 0 probability for all classes with observation 4517Numerical 0 probability for all classes with observation 4558Numerical 0 probability for all classes with observation 4742Numerical 0 probability for all classes with observation 4746Numerical 0 probability for all classes with observation 4784Numerical 0 probability for all classes with observation 4861Numerical 0 probability for all classes with observation 5173Numerical 0 probability for all classes with observation 5212Numerical 0 probability for all classes with observation 5391Numerical 0 probability for all classes with observation 5453Numerical 0 probability for all classes with observation 5591Numerical 0 probability for all classes with observation 5656Numerical 0 probability for all classes with observation 5723Numerical 0 probability for all classes with observation 5853Numerical 0 probability for all classes with observation 5858Numerical 0 probability for all classes with observation 6220Numerical 0 probability for all classes with observation 6226Numerical 0 probability for all classes with observation 6396Numerical 0 probability for all classes with observation 6468Numerical 0 probability for all classes with observation 6659Numerical 0 probability for all classes with observation 6678Numerical 0 probability for all classes with observation 6696Numerical 0 probability for all classes with observation 6699Numerical 0 probability for all classes with observation 6823Numerical 0 probability for all classes with observation 6932Numerical 0 probability for all classes with observation 7141Numerical 0 probability for all classes with observation 7631Numerical 0 probability for all classes with observation 7795Numerical 0 probability for all classes with observation 7907Numerical 0 probability for all classes with observation 7927Numerical 0 probability for all classes with observation 8331Numerical 0 probability for all classes with observation 8497Numerical 0 probability for all classes with observation 8572Numerical 0 probability for all classes with observation 8794Numerical 0 probability for all classes with observation 8970Numerical 0 probability for all classes with observation 9149Numerical 0 probability for all classes with observation 9190Numerical 0 probability for all classes with observation 9328Numerical 0 probability for all classes with observation 9334Numerical 0 probability for all classes with observation 9388Numerical 0 probability for all classes with observation 9690Numerical 0 probability for all classes with observation 9833Numerical 0 probability for all classes with observation 9940Numerical 0 probability for all classes with observation 10307Numerical 0 probability for all classes with observation 10324Numerical 0 probability for all classes with observation 10908Numerical 0 probability for all classes with observation 10964Numerical 0 probability for all classes with observation 10977Numerical 0 probability for all classes with observation 11022Numerical 0 probability for all classes with observation 11098Numerical 0 probability for all classes with observation 11198Numerical 0 probability for all classes with observation 11481Numerical 0 probability for all classes with observation 11498Numerical 0 probability for all classes with observation 11571Numerical 0 probability for all classes with observation 11911Numerical 0 probability for all classes with observation 12083Numerical 0 probability for all classes with observation 12289Numerical 0 probability for all classes with observation 12316Numerical 0 probability for all classes with observation 12464Numerical 0 probability for all classes with observation 12527Numerical 0 probability for all classes with observation 12550Numerical 0 probability for all classes with observation 12576Numerical 0 probability for all classes with observation 12650Numerical 0 probability for all classes with observation 12662Numerical 0 probability for all classes with observation 12679Numerical 0 probability for all classes with observation 12938Numerical 0 probability for all classes with observation 13014Numerical 0 probability for all classes with observation 13339Numerical 0 probability for all classes with observation 13443Numerical 0 probability for all classes with observation 13558Numerical 0 probability for all classes with observation 13577Numerical 0 probability for all classes with observation 13721Numerical 0 probability for all classes with observation 13871Numerical 0 probability for all classes with observation 14008Numerical 0 probability for all classes with observation 14206Numerical 0 probability for all classes with observation 14290Numerical 0 probability for all classes with observation 14688Numerical 0 probability for all classes with observation 15167Numerical 0 probability for all classes with observation 15172Numerical 0 probability for all classes with observation 15195Numerical 0 probability for all classes with observation 15251

predictionNB = predict(modelNB, data_test[,-13])

Numerical 0 probability for all classes with observation 171Numerical 0 probability for all classes with observation 177Numerical 0 probability for all classes with observation 53517Numerical 0 probability for all classes with observation 75321

confusionMatrix(predictionNB, data_test$classLabel)

Confusion Matrix and Statistics

          Reference
Prediction     1     2     3
         1 53782   303  1459
         2    11  8332  1223
         3    14    52 36737

Overall Statistics
                                         
               Accuracy : 0.97           
                 95% CI : (0.9689, 0.971)
    No Information Rate : 0.528          
    P-Value [Acc > NIR] : < 2.2e-16      
                                         
                  Kappa : 0.9468         
                                         
 Mcnemar's Test P-Value : < 2.2e-16      

Statistics by Class:

                     Class: 1 Class: 2 Class: 3
Sensitivity            0.9995  0.95913   0.9320
Specificity            0.9634  0.98676   0.9989
Pos Pred Value         0.9683  0.87100   0.9982
Neg Pred Value         0.9995  0.99616   0.9588
Prevalence             0.5280  0.08524   0.3868
Detection Rate         0.5277  0.08176   0.3605
Detection Prevalence   0.5450  0.09386   0.3611
Balanced Accuracy      0.9815  0.97295   0.9655

Naive bayes with cross validation and feature selection

data_train <- na.omit(dataForNaiveBayes[ trainIndex,])
data_test <- na.omit(dataForNaiveBayes[-trainIndex,])
#feature selection - removed content.rating and type - low feature importance
col <-c(2,3,4,5,6,7,12)
x<-data_train[,col]
y<-data_train$classLabel
modelNB = train(x,y,'nb',trControl=trainControl(method='cv',number=10))

Numerical 0 probability for all classes with observation 8957Numerical 0 probability for all classes with observation 781Numerical 0 probability for all classes with observation 1017Numerical 0 probability for all classes with observation 1109Numerical 0 probability for all classes with observation 1261Numerical 0 probability for all classes with observation 1538Numerical 0 probability for all classes with observation 1800Numerical 0 probability for all classes with observation 1942Numerical 0 probability for all classes with observation 2229Numerical 0 probability for all classes with observation 2257Numerical 0 probability for all classes with observation 2991Numerical 0 probability for all classes with observation 3106Numerical 0 probability for all classes with observation 3417Numerical 0 probability for all classes with observation 3562Numerical 0 probability for all classes with observation 3757Numerical 0 probability for all classes with observation 4040Numerical 0 probability for all classes with observation 4074Numerical 0 probability for all classes with observation 4427Numerical 0 probability for all classes with observation 4486Numerical 0 probability for all classes with observation 4587Numerical 0 probability for all classes with observation 4634Numerical 0 probability for all classes with observation 4643Numerical 0 probability for all classes with observation 4672Numerical 0 probability for all classes with observation 4720Numerical 0 probability for all classes with observation 4860Numerical 0 probability for all classes with observation 5392Numerical 0 probability for all classes with observation 5462Numerical 0 probability for all classes with observation 5586Numerical 0 probability for all classes with observation 5609Numerical 0 probability for all classes with observation 5685Numerical 0 probability for all classes with observation 5856Numerical 0 probability for all classes with observation 5893Numerical 0 probability for all classes with observation 5935Numerical 0 probability for all classes with observation 6157Numerical 0 probability for all classes with observation 6319Numerical 0 probability for all classes with observation 6453Numerical 0 probability for all classes with observation 6768Numerical 0 probability for all classes with observation 7284Numerical 0 probability for all classes with observation 7326Numerical 0 probability for all classes with observation 7505Numerical 0 probability for all classes with observation 7636Numerical 0 probability for all classes with observation 7663Numerical 0 probability for all classes with observation 7833Numerical 0 probability for all classes with observation 8325Numerical 0 probability for all classes with observation 8472Numerical 0 probability for all classes with observation 8547Numerical 0 probability for all classes with observation 8555Numerical 0 probability for all classes with observation 8621Numerical 0 probability for all classes with observation 8957Numerical 0 probability for all classes with observation 9154Numerical 0 probability for all classes with observation 9722Numerical 0 probability for all classes with observation 9792Numerical 0 probability for all classes with observation 9927Numerical 0 probability for all classes with observation 10087Numerical 0 probability for all classes with observation 10157Numerical 0 probability for all classes with observation 10209Numerical 0 probability for all classes with observation 10212Numerical 0 probability for all classes with observation 10305Numerical 0 probability for all classes with observation 10368Numerical 0 probability for all classes with observation 10658Numerical 0 probability for all classes with observation 11080Numerical 0 probability for all classes with observation 11259Numerical 0 probability for all classes with observation 11484Numerical 0 probability for all classes with observation 11540Numerical 0 probability for all classes with observation 11585Numerical 0 probability for all classes with observation 11777Numerical 0 probability for all classes with observation 11943Numerical 0 probability for all classes with observation 12096Numerical 0 probability for all classes with observation 12613Numerical 0 probability for all classes with observation 12831Numerical 0 probability for all classes with observation 12864Numerical 0 probability for all classes with observation 12972Numerical 0 probability for all classes with observation 13007Numerical 0 probability for all classes with observation 13281Numerical 0 probability for all classes with observation 13329Numerical 0 probability for all classes with observation 13419Numerical 0 probability for all classes with observation 13430Numerical 0 probability for all classes with observation 14438Numerical 0 probability for all classes with observation 14649Numerical 0 probability for all classes with observation 14748Numerical 0 probability for all classes with observation 15208Numerical 0 probability for all classes with observation 3529Numerical 0 probability for all classes with observation 601Numerical 0 probability for all classes with observation 661Numerical 0 probability for all classes with observation 702Numerical 0 probability for all classes with observation 736Numerical 0 probability for all classes with observation 1404Numerical 0 probability for all classes with observation 1425Numerical 0 probability for all classes with observation 1653Numerical 0 probability for all classes with observation 1847Numerical 0 probability for all classes with observation 2108Numerical 0 probability for all classes with observation 2178Numerical 0 probability for all classes with observation 2409Numerical 0 probability for all classes with observation 2768Numerical 0 probability for all classes with observation 2900Numerical 0 probability for all classes with observation 3155Numerical 0 probability for all classes with observation 3232Numerical 0 probability for all classes with observation 4069Numerical 0 probability for all classes with observation 4250Numerical 0 probability for all classes with observation 4443Numerical 0 probability for all classes with observation 4698Numerical 0 probability for all classes with observation 4843Numerical 0 probability for all classes with observation 4958Numerical 0 probability for all classes with observation 5113Numerical 0 probability for all classes with observation 5144Numerical 0 probability for all classes with observation 5225Numerical 0 probability for all classes with observation 5534Numerical 0 probability for all classes with observation 5645Numerical 0 probability for all classes with observation 5883Numerical 0 probability for all classes with observation 6007Numerical 0 probability for all classes with observation 6181Numerical 0 probability for all classes with observation 6246Numerical 0 probability for all classes with observation 6273Numerical 0 probability for all classes with observation 6592Numerical 0 probability for all classes with observation 6983Numerical 0 probability for all classes with observation 7039Numerical 0 probability for all classes with observation 7129Numerical 0 probability for all classes with observation 7273Numerical 0 probability for all classes with observation 7275Numerical 0 probability for all classes with observation 7460Numerical 0 probability for all classes with observation 7513Numerical 0 probability for all classes with observation 7730Numerical 0 probability for all classes with observation 7938Numerical 0 probability for all classes with observation 8234Numerical 0 probability for all classes with observation 8413Numerical 0 probability for all classes with observation 8440Numerical 0 probability for all classes with observation 8462Numerical 0 probability for all classes with observation 8773Numerical 0 probability for all classes with observation 8847Numerical 0 probability for all classes with observation 8960Numerical 0 probability for all classes with observation 8979Numerical 0 probability for all classes with observation 9143Numerical 0 probability for all classes with observation 9171Numerical 0 probability for all classes with observation 9540Numerical 0 probability for all classes with observation 9952Numerical 0 probability for all classes with observation 10128Numerical 0 probability for all classes with observation 10156Numerical 0 probability for all classes with observation 10182Numerical 0 probability for all classes with observation 10227Numerical 0 probability for all classes with observation 10683Numerical 0 probability for all classes with observation 10751Numerical 0 probability for all classes with observation 10949Numerical 0 probability for all classes with observation 11200Numerical 0 probability for all classes with observation 11489Numerical 0 probability for all classes with observation 11514Numerical 0 probability for all classes with observation 11602Numerical 0 probability for all classes with observation 12076Numerical 0 probability for all classes with observation 12119Numerical 0 probability for all classes with observation 12458Numerical 0 probability for all classes with observation 12477Numerical 0 probability for all classes with observation 12848Numerical 0 probability for all classes with observation 12957Numerical 0 probability for all classes with observation 13019Numerical 0 probability for all classes with observation 13103Numerical 0 probability for all classes with observation 13275Numerical 0 probability for all classes with observation 13454Numerical 0 probability for all classes with observation 13843Numerical 0 probability for all classes with observation 13858Numerical 0 probability for all classes with observation 14348Numerical 0 probability for all classes with observation 14372Numerical 0 probability for all classes with observation 14509Numerical 0 probability for all classes with observation 14653Numerical 0 probability for all classes with observation 14681Numerical 0 probability for all classes with observation 15155Numerical 0 probability for all classes with observation 15193Numerical 0 probability for all classes with observation 15210Numerical 0 probability for all classes with observation 15253Numerical 0 probability for all classes with observation 350Numerical 0 probability for all classes with observation 379Numerical 0 probability for all classes with observation 417Numerical 0 probability for all classes with observation 654Numerical 0 probability for all classes with observation 660Numerical 0 probability for all classes with observation 766Numerical 0 probability for all classes with observation 1367Numerical 0 probability for all classes with observation 1403Numerical 0 probability for all classes with observation 1861Numerical 0 probability for all classes with observation 1916Numerical 0 probability for all classes with observation 2024Numerical 0 probability for all classes with observation 2223Numerical 0 probability for all classes with observation 2311Numerical 0 probability for all classes with observation 2388Numerical 0 probability for all classes with observation 2592Numerical 0 probability for all classes with observation 3095Numerical 0 probability for all classes with observation 3219Numerical 0 probability for all classes with observation 3305Numerical 0 probability for all classes with observation 3491Numerical 0 probability for all classes with observation 3552Numerical 0 probability for all classes with observation 3706Numerical 0 probability for all classes with observation 3853Numerical 0 probability for all classes with observation 3862Numerical 0 probability for all classes with observation 3958Numerical 0 probability for all classes with observation 4073Numerical 0 probability for all classes with observation 4127Numerical 0 probability for all classes with observation 4375Numerical 0 probability for all classes with observation 4377Numerical 0 probability for all classes with observation 4412Numerical 0 probability for all classes with observation 4715Numerical 0 probability for all classes with observation 4909Numerical 0 probability for all classes with observation 5142Numerical 0 probability for all classes with observation 5290Numerical 0 probability for all classes with observation 5460Numerical 0 probability for all classes with observation 6122Numerical 0 probability for all classes with observation 6273Numerical 0 probability for all classes with observation 6377Numerical 0 probability for all classes with observation 6535Numerical 0 probability for all classes with observation 6565Numerical 0 probability for all classes with observation 7094Numerical 0 probability for all classes with observation 7350Numerical 0 probability for all classes with observation 7536Numerical 0 probability for all classes with observation 7670Numerical 0 probability for all classes with observation 7686Numerical 0 probability for all classes with observation 7746Numerical 0 probability for all classes with observation 7771Numerical 0 probability for all classes with observation 7830Numerical 0 probability for all classes with observation 7850Numerical 0 probability for all classes with observation 8207Numerical 0 probability for all classes with observation 8631Numerical 0 probability for all classes with observation 8668Numerical 0 probability for all classes with observation 9594Numerical 0 probability for all classes with observation 9606Numerical 0 probability for all classes with observation 9961Numerical 0 probability for all classes with observation 10452Numerical 0 probability for all classes with observation 10630Numerical 0 probability for all classes with observation 10747Numerical 0 probability for all classes with observation 10871Numerical 0 probability for all classes with observation 11022Numerical 0 probability for all classes with observation 11135Numerical 0 probability for all classes with observation 11402Numerical 0 probability for all classes with observation 11416Numerical 0 probability for all classes with observation 11500Numerical 0 probability for all classes with observation 12267Numerical 0 probability for all classes with observation 12303Numerical 0 probability for all classes with observation 12342Numerical 0 probability for all classes with observation 12863Numerical 0 probability for all classes with observation 13077Numerical 0 probability for all classes with observation 13378Numerical 0 probability for all classes with observation 13560Numerical 0 probability for all classes with observation 13608Numerical 0 probability for all classes with observation 13735Numerical 0 probability for all classes with observation 13737Numerical 0 probability for all classes with observation 13779Numerical 0 probability for all classes with observation 13851Numerical 0 probability for all classes with observation 14009Numerical 0 probability for all classes with observation 14022Numerical 0 probability for all classes with observation 14223Numerical 0 probability for all classes with observation 14363Numerical 0 probability for all classes with observation 14384Numerical 0 probability for all classes with observation 14605Numerical 0 probability for all classes with observation 14621Numerical 0 probability for all classes with observation 14800Numerical 0 probability for all classes with observation 532Numerical 0 probability for all classes with observation 756Numerical 0 probability for all classes with observation 981Numerical 0 probability for all classes with observation 1086Numerical 0 probability for all classes with observation 1107Numerical 0 probability for all classes with observation 1167Numerical 0 probability for all classes with observation 1813Numerical 0 probability for all classes with observation 2434Numerical 0 probability for all classes with observation 2529Numerical 0 probability for all classes with observation 2843Numerical 0 probability for all classes with observation 3134Numerical 0 probability for all classes with observation 3408Numerical 0 probability for all classes with observation 3438Numerical 0 probability for all classes with observation 3481Numerical 0 probability for all classes with observation 3572Numerical 0 probability for all classes with observation 3741Numerical 0 probability for all classes with observation 3847Numerical 0 probability for all classes with observation 3947Numerical 0 probability for all classes with observation 4186Numerical 0 probability for all classes with observation 4366Numerical 0 probability for all classes with observation 4661Numerical 0 probability for all classes with observation 4875Numerical 0 probability for all classes with observation 4906Numerical 0 probability for all classes with observation 5012Numerical 0 probability for all classes with observation 5154Numerical 0 probability for all classes with observation 5233Numerical 0 probability for all classes with observation 5941Numerical 0 probability for all classes with observation 6544Numerical 0 probability for all classes with observation 6627Numerical 0 probability for all classes with observation 6822Numerical 0 probability for all classes with observation 7207Numerical 0 probability for all classes with observation 7378Numerical 0 probability for all classes with observation 7501Numerical 0 probability for all classes with observation 7712Numerical 0 probability for all classes with observation 7751Numerical 0 probability for all classes with observation 7980Numerical 0 probability for all classes with observation 8454Numerical 0 probability for all classes with observation 8466Numerical 0 probability for all classes with observation 8487Numerical 0 probability for all classes with observation 8573Numerical 0 probability for all classes with observation 8660Numerical 0 probability for all classes with observation 8810Numerical 0 probability for all classes with observation 9562Numerical 0 probability for all classes with observation 9655Numerical 0 probability for all classes with observation 10303Numerical 0 probability for all classes with observation 10353Numerical 0 probability for all classes with observation 10675Numerical 0 probability for all classes with observation 10980Numerical 0 probability for all classes with observation 11096Numerical 0 probability for all classes with observation 11305Numerical 0 probability for all classes with observation 11562Numerical 0 probability for all classes with observation 12003Numerical 0 probability for all classes with observation 12351Numerical 0 probability for all classes with observation 12450Numerical 0 probability for all classes with observation 12591Numerical 0 probability for all classes with observation 13074Numerical 0 probability for all classes with observation 13277Numerical 0 probability for all classes with observation 13310Numerical 0 probability for all classes with observation 13333Numerical 0 probability for all classes with observation 13559Numerical 0 probability for all classes with observation 13663Numerical 0 probability for all classes with observation 13866Numerical 0 probability for all classes with observation 14437Numerical 0 probability for all classes with observation 15066Numerical 0 probability for all classes with observation 15084Numerical 0 probability for all classes with observation 15166Numerical 0 probability for all classes with observation 15191Numerical 0 probability for all classes with observation 157Numerical 0 probability for all classes with observation 324Numerical 0 probability for all classes with observation 381Numerical 0 probability for all classes with observation 934Numerical 0 probability for all classes with observation 972Numerical 0 probability for all classes with observation 1068Numerical 0 probability for all classes with observation 1072Numerical 0 probability for all classes with observation 1088Numerical 0 probability for all classes with observation 1436Numerical 0 probability for all classes with observation 1882Numerical 0 probability for all classes with observation 2019Numerical 0 probability for all classes with observation 2195Numerical 0 probability for all classes with observation 2227Numerical 0 probability for all classes with observation 2697Numerical 0 probability for all classes with observation 2772Numerical 0 probability for all classes with observation 2804Numerical 0 probability for all classes with observation 3075Numerical 0 probability for all classes with observation 3350Numerical 0 probability for all classes with observation 3513Numerical 0 probability for all classes with observation 4206Numerical 0 probability for all classes with observation 4280Numerical 0 probability for all classes with observation 4355Numerical 0 probability for all classes with observation 4551Numerical 0 probability for all classes with observation 4874Numerical 0 probability for all classes with observation 4980Numerical 0 probability for all classes with observation 5709Numerical 0 probability for all classes with observation 5758Numerical 0 probability for all classes with observation 5974Numerical 0 probability for all classes with observation 5990Numerical 0 probability for all classes with observation 6439Numerical 0 probability for all classes with observation 6615Numerical 0 probability for all classes with observation 6742Numerical 0 probability for all classes with observation 6841Numerical 0 probability for all classes with observation 6956Numerical 0 probability for all classes with observation 7751Numerical 0 probability for all classes with observation 7915Numerical 0 probability for all classes with observation 8035Numerical 0 probability for all classes with observation 8188Numerical 0 probability for all classes with observation 8511Numerical 0 probability for all classes with observation 8631Numerical 0 probability for all classes with observation 8726Numerical 0 probability for all classes with observation 9079Numerical 0 probability for all classes with observation 9135Numerical 0 probability for all classes with observation 9240Numerical 0 probability for all classes with observation 9290Numerical 0 probability for all classes with observation 9335Numerical 0 probability for all classes with observation 9609Numerical 0 probability for all classes with observation 10575Numerical 0 probability for all classes with observation 10805Numerical 0 probability for all classes with observation 10904Numerical 0 probability for all classes with observation 10988Numerical 0 probability for all classes with observation 11079Numerical 0 probability for all classes with observation 11571Numerical 0 probability for all classes with observation 11974Numerical 0 probability for all classes with observation 12469Numerical 0 probability for all classes with observation 12608Numerical 0 probability for all classes with observation 12743Numerical 0 probability for all classes with observation 12855Numerical 0 probability for all classes with observation 12945Numerical 0 probability for all classes with observation 13386Numerical 0 probability for all classes with observation 13444Numerical 0 probability for all classes with observation 13475Numerical 0 probability for all classes with observation 13854Numerical 0 probability for all classes with observation 13912Numerical 0 probability for all classes with observation 14249Numerical 0 probability for all classes with observation 14555Numerical 0 probability for all classes with observation 14701Numerical 0 probability for all classes with observation 14802Numerical 0 probability for all classes with observation 14854Numerical 0 probability for all classes with observation 15062Numerical 0 probability for all classes with observation 15121Numerical 0 probability for all classes with observation 307Numerical 0 probability for all classes with observation 443Numerical 0 probability for all classes with observation 493Numerical 0 probability for all classes with observation 526Numerical 0 probability for all classes with observation 750Numerical 0 probability for all classes with observation 769Numerical 0 probability for all classes with observation 776Numerical 0 probability for all classes with observation 848Numerical 0 probability for all classes with observation 1079Numerical 0 probability for all classes with observation 1151Numerical 0 probability for all classes with observation 1321Numerical 0 probability for all classes with observation 1771Numerical 0 probability for all classes with observation 1814Numerical 0 probability for all classes with observation 1837Numerical 0 probability for all classes with observation 2199Numerical 0 probability for all classes with observation 2218Numerical 0 probability for all classes with observation 2219Numerical 0 probability for all classes with observation 2721Numerical 0 probability for all classes with observation 3243Numerical 0 probability for all classes with observation 3391Numerical 0 probability for all classes with observation 3714Numerical 0 probability for all classes with observation 4630Numerical 0 probability for all classes with observation 4749Numerical 0 probability for all classes with observation 5216Numerical 0 probability for all classes with observation 5340Numerical 0 probability for all classes with observation 5504Numerical 0 probability for all classes with observation 5649Numerical 0 probability for all classes with observation 5909Numerical 0 probability for all classes with observation 5936Numerical 0 probability for all classes with observation 6162Numerical 0 probability for all classes with observation 6179Numerical 0 probability for all classes with observation 6536Numerical 0 probability for all classes with observation 6885Numerical 0 probability for all classes with observation 7336Numerical 0 probability for all classes with observation 7404Numerical 0 probability for all classes with observation 7410Numerical 0 probability for all classes with observation 7432Numerical 0 probability for all classes with observation 7653Numerical 0 probability for all classes with observation 8068Numerical 0 probability for all classes with observation 8274Numerical 0 probability for all classes with observation 9105Numerical 0 probability for all classes with observation 9467Numerical 0 probability for all classes with observation 9572Numerical 0 probability for all classes with observation 9660Numerical 0 probability for all classes with observation 9766Numerical 0 probability for all classes with observation 10107Numerical 0 probability for all classes with observation 10220Numerical 0 probability for all classes with observation 10296Numerical 0 probability for all classes with observation 10736Numerical 0 probability for all classes with observation 11233Numerical 0 probability for all classes with observation 11268Numerical 0 probability for all classes with observation 11350Numerical 0 probability for all classes with observation 11368Numerical 0 probability for all classes with observation 11520Numerical 0 probability for all classes with observation 11536Numerical 0 probability for all classes with observation 11707Numerical 0 probability for all classes with observation 11750Numerical 0 probability for all classes with observation 11856Numerical 0 probability for all classes with observation 11969Numerical 0 probability for all classes with observation 12283Numerical 0 probability for all classes with observation 12391Numerical 0 probability for all classes with observation 12736Numerical 0 probability for all classes with observation 13594Numerical 0 probability for all classes with observation 13631Numerical 0 probability for all classes with observation 13772Numerical 0 probability for all classes with observation 14223Numerical 0 probability for all classes with observation 14312Numerical 0 probability for all classes with observation 15027Numerical 0 probability for all classes with observation 15258Numerical 0 probability for all classes with observation 192Numerical 0 probability for all classes with observation 535Numerical 0 probability for all classes with observation 725Numerical 0 probability for all classes with observation 852Numerical 0 probability for all classes with observation 1550Numerical 0 probability for all classes with observation 1629Numerical 0 probability for all classes with observation 1636Numerical 0 probability for all classes with observation 1742Numerical 0 probability for all classes with observation 1798Numerical 0 probability for all classes with observation 1827Numerical 0 probability for all classes with observation 2062Numerical 0 probability for all classes with observation 2441Numerical 0 probability for all classes with observation 2475Numerical 0 probability for all classes with observation 2539Numerical 0 probability for all classes with observation 2748Numerical 0 probability for all classes with observation 2853Numerical 0 probability for all classes with observation 3232Numerical 0 probability for all classes with observation 3519Numerical 0 probability for all classes with observation 3535Numerical 0 probability for all classes with observation 3687Numerical 0 probability for all classes with observation 3695Numerical 0 probability for all classes with observation 3746Numerical 0 probability for all classes with observation 3805Numerical 0 probability for all classes with observation 3929Numerical 0 probability for all classes with observation 4343Numerical 0 probability for all classes with observation 5084Numerical 0 probability for all classes with observation 5160Numerical 0 probability for all classes with observation 5327Numerical 0 probability for all classes with observation 5717Numerical 0 probability for all classes with observation 6112Numerical 0 probability for all classes with observation 6129Numerical 0 probability for all classes with observation 6541Numerical 0 probability for all classes with observation 6646Numerical 0 probability for all classes with observation 6788Numerical 0 probability for all classes with observation 7338Numerical 0 probability for all classes with observation 7385Numerical 0 probability for all classes with observation 7624Numerical 0 probability for all classes with observation 7713Numerical 0 probability for all classes with observation 7890Numerical 0 probability for all classes with observation 7910Numerical 0 probability for all classes with observation 8445Numerical 0 probability for all classes with observation 8552Numerical 0 probability for all classes with observation 9065Numerical 0 probability for all classes with observation 9129Numerical 0 probability for all classes with observation 9226Numerical 0 probability for all classes with observation 9485Numerical 0 probability for all classes with observation 9549Numerical 0 probability for all classes with observation 9717Numerical 0 probability for all classes with observation 10101Numerical 0 probability for all classes with observation 10349Numerical 0 probability for all classes with observation 10993Numerical 0 probability for all classes with observation 11251Numerical 0 probability for all classes with observation 11524Numerical 0 probability for all classes with observation 11573Numerical 0 probability for all classes with observation 11579Numerical 0 probability for all classes with observation 11755Numerical 0 probability for all classes with observation 11823Numerical 0 probability for all classes with observation 11936Numerical 0 probability for all classes with observation 11952Numerical 0 probability for all classes with observation 12247Numerical 0 probability for all classes with observation 12256Numerical 0 probability for all classes with observation 12697Numerical 0 probability for all classes with observation 12701Numerical 0 probability for all classes with observation 12878Numerical 0 probability for all classes with observation 13164Numerical 0 probability for all classes with observation 13225Numerical 0 probability for all classes with observation 13462Numerical 0 probability for all classes with observation 14396Numerical 0 probability for all classes with observation 14475Numerical 0 probability for all classes with observation 14657Numerical 0 probability for all classes with observation 14665Numerical 0 probability for all classes with observation 14686Numerical 0 probability for all classes with observation 14716Numerical 0 probability for all classes with observation 15021Numerical 0 probability for all classes with observation 15267Numerical 0 probability for all classes with observation 185Numerical 0 probability for all classes with observation 292Numerical 0 probability for all classes with observation 367Numerical 0 probability for all classes with observation 638Numerical 0 probability for all classes with observation 707Numerical 0 probability for all classes with observation 722Numerical 0 probability for all classes with observation 1624Numerical 0 probability for all classes with observation 1869Numerical 0 probability for all classes with observation 1936Numerical 0 probability for all classes with observation 2056Numerical 0 probability for all classes with observation 2087Numerical 0 probability for all classes with observation 2255Numerical 0 probability for all classes with observation 2782Numerical 0 probability for all classes with observation 2878Numerical 0 probability for all classes with observation 3376Numerical 0 probability for all classes with observation 3438Numerical 0 probability for all classes with observation 3465Numerical 0 probability for all classes with observation 3662Numerical 0 probability for all classes with observation 3667Numerical 0 probability for all classes with observation 3764Numerical 0 probability for all classes with observation 3892Numerical 0 probability for all classes with observation 3919Numerical 0 probability for all classes with observation 3985Numerical 0 probability for all classes with observation 4050Numerical 0 probability for all classes with observation 4803Numerical 0 probability for all classes with observation 5219Numerical 0 probability for all classes with observation 5235Numerical 0 probability for all classes with observation 5282Numerical 0 probability for all classes with observation 5546Numerical 0 probability for all classes with observation 5628Numerical 0 probability for all classes with observation 6270Numerical 0 probability for all classes with observation 6292Numerical 0 probability for all classes with observation 6540Numerical 0 probability for all classes with observation 6644Numerical 0 probability for all classes with observation 6668Numerical 0 probability for all classes with observation 6733Numerical 0 probability for all classes with observation 6963Numerical 0 probability for all classes with observation 6984Numerical 0 probability for all classes with observation 7237Numerical 0 probability for all classes with observation 7499Numerical 0 probability for all classes with observation 7606Numerical 0 probability for all classes with observation 7668Numerical 0 probability for all classes with observation 7711Numerical 0 probability for all classes with observation 8041Numerical 0 probability for all classes with observation 8669Numerical 0 probability for all classes with observation 9166Numerical 0 probability for all classes with observation 9543Numerical 0 probability for all classes with observation 9614Numerical 0 probability for all classes with observation 10744Numerical 0 probability for all classes with observation 10843Numerical 0 probability for all classes with observation 11007Numerical 0 probability for all classes with observation 11942Numerical 0 probability for all classes with observation 12057Numerical 0 probability for all classes with observation 12088Numerical 0 probability for all classes with observation 12202Numerical 0 probability for all classes with observation 12714Numerical 0 probability for all classes with observation 12947Numerical 0 probability for all classes with observation 13312Numerical 0 probability for all classes with observation 13723Numerical 0 probability for all classes with observation 14211Numerical 0 probability for all classes with observation 14480Numerical 0 probability for all classes with observation 14529Numerical 0 probability for all classes with observation 14814Numerical 0 probability for all classes with observation 14819Numerical 0 probability for all classes with observation 15088Numerical 0 probability for all classes with observation 15101Numerical 0 probability for all classes with observation 15142Numerical 0 probability for all classes with observation 15178Numerical 0 probability for all classes with observation 113Numerical 0 probability for all classes with observation 130Numerical 0 probability for all classes with observation 164Numerical 0 probability for all classes with observation 583Numerical 0 probability for all classes with observation 1500Numerical 0 probability for all classes with observation 1588Numerical 0 probability for all classes with observation 1610Numerical 0 probability for all classes with observation 1676Numerical 0 probability for all classes with observation 2088Numerical 0 probability for all classes with observation 2255Numerical 0 probability for all classes with observation 2497Numerical 0 probability for all classes with observation 4027Numerical 0 probability for all classes with observation 4155Numerical 0 probability for all classes with observation 4388Numerical 0 probability for all classes with observation 4509Numerical 0 probability for all classes with observation 5089Numerical 0 probability for all classes with observation 5232Numerical 0 probability for all classes with observation 5294Numerical 0 probability for all classes with observation 5377Numerical 0 probability for all classes with observation 5621Numerical 0 probability for all classes with observation 7003Numerical 0 probability for all classes with observation 7623Numerical 0 probability for all classes with observation 7639Numerical 0 probability for all classes with observation 7728Numerical 0 probability for all classes with observation 8078Numerical 0 probability for all classes with observation 8215Numerical 0 probability for all classes with observation 8296Numerical 0 probability for all classes with observation 8586Numerical 0 probability for all classes with observation 8755Numerical 0 probability for all classes with observation 8916Numerical 0 probability for all classes with observation 9296Numerical 0 probability for all classes with observation 9643Numerical 0 probability for all classes with observation 9750Numerical 0 probability for all classes with observation 9963Numerical 0 probability for all classes with observation 9990Numerical 0 probability for all classes with observation 10117Numerical 0 probability for all classes with observation 10359Numerical 0 probability for all classes with observation 10548Numerical 0 probability for all classes with observation 10875Numerical 0 probability for all classes with observation 11090Numerical 0 probability for all classes with observation 11152Numerical 0 probability for all classes with observation 11591Numerical 0 probability for all classes with observation 11873Numerical 0 probability for all classes with observation 12108Numerical 0 probability for all classes with observation 12187Numerical 0 probability for all classes with observation 12407Numerical 0 probability for all classes with observation 12600Numerical 0 probability for all classes with observation 13171Numerical 0 probability for all classes with observation 13311Numerical 0 probability for all classes with observation 13318Numerical 0 probability for all classes with observation 13335Numerical 0 probability for all classes with observation 13587Numerical 0 probability for all classes with observation 13784Numerical 0 probability for all classes with observation 13989Numerical 0 probability for all classes with observation 14008Numerical 0 probability for all classes with observation 14364Numerical 0 probability for all classes with observation 14678Numerical 0 probability for all classes with observation 14931Numerical 0 probability for all classes with observation 40Numerical 0 probability for all classes with observation 48Numerical 0 probability for all classes with observation 397Numerical 0 probability for all classes with observation 583Numerical 0 probability for all classes with observation 749Numerical 0 probability for all classes with observation 1501Numerical 0 probability for all classes with observation 1736Numerical 0 probability for all classes with observation 1910Numerical 0 probability for all classes with observation 1940Numerical 0 probability for all classes with observation 2021Numerical 0 probability for all classes with observation 2179Numerical 0 probability for all classes with observation 2473Numerical 0 probability for all classes with observation 2882Numerical 0 probability for all classes with observation 2894Numerical 0 probability for all classes with observation 3105Numerical 0 probability for all classes with observation 3145Numerical 0 probability for all classes with observation 3190Numerical 0 probability for all classes with observation 3312Numerical 0 probability for all classes with observation 3316Numerical 0 probability for all classes with observation 3447Numerical 0 probability for all classes with observation 4018Numerical 0 probability for all classes with observation 4043Numerical 0 probability for all classes with observation 4049Numerical 0 probability for all classes with observation 4273Numerical 0 probability for all classes with observation 4499Numerical 0 probability for all classes with observation 4675Numerical 0 probability for all classes with observation 4731Numerical 0 probability for all classes with observation 5318Numerical 0 probability for all classes with observation 5667Numerical 0 probability for all classes with observation 5702Numerical 0 probability for all classes with observation 5835Numerical 0 probability for all classes with observation 6180Numerical 0 probability for all classes with observation 6378Numerical 0 probability for all classes with observation 6420Numerical 0 probability for all classes with observation 6825Numerical 0 probability for all classes with observation 6973Numerical 0 probability for all classes with observation 7287Numerical 0 probability for all classes with observation 7651Numerical 0 probability for all classes with observation 7712Numerical 0 probability for all classes with observation 7772Numerical 0 probability for all classes with observation 8010Numerical 0 probability for all classes with observation 8376Numerical 0 probability for all classes with observation 8525Numerical 0 probability for all classes with observation 8978Numerical 0 probability for all classes with observation 9089Numerical 0 probability for all classes with observation 9185Numerical 0 probability for all classes with observation 9761Numerical 0 probability for all classes with observation 9842Numerical 0 probability for all classes with observation 9912Numerical 0 probability for all classes with observation 10653Numerical 0 probability for all classes with observation 10964Numerical 0 probability for all classes with observation 11226Numerical 0 probability for all classes with observation 11802Numerical 0 probability for all classes with observation 11824Numerical 0 probability for all classes with observation 12222Numerical 0 probability for all classes with observation 12430Numerical 0 probability for all classes with observation 12475Numerical 0 probability for all classes with observation 12800Numerical 0 probability for all classes with observation 13103Numerical 0 probability for all classes with observation 13188Numerical 0 probability for all classes with observation 13250Numerical 0 probability for all classes with observation 13316Numerical 0 probability for all classes with observation 13357Numerical 0 probability for all classes with observation 13462Numerical 0 probability for all classes with observation 13476Numerical 0 probability for all classes with observation 13490Numerical 0 probability for all classes with observation 13495Numerical 0 probability for all classes with observation 13564Numerical 0 probability for all classes with observation 14049Numerical 0 probability for all classes with observation 14130Numerical 0 probability for all classes with observation 14685Numerical 0 probability for all classes with observation 14850Numerical 0 probability for all classes with observation 15061

predictionNB = predict(modelNB, data_test[,-13])

Numerical 0 probability for all classes with observation 171Numerical 0 probability for all classes with observation 53517Numerical 0 probability for all classes with observation 75321

confusionMatrix(predictionNB, data_test$classLabel)

Confusion Matrix and Statistics

          Reference
Prediction     1     2     3
         1 53781   302  1457
         2    12  8334  1215
         3    14    51 36747

Overall Statistics
                                         
               Accuracy : 0.9701         
                 95% CI : (0.969, 0.9711)
    No Information Rate : 0.528          
    P-Value [Acc > NIR] : < 2.2e-16      
                                         
                  Kappa : 0.947          
                                         
 Mcnemar's Test P-Value : < 2.2e-16      

Statistics by Class:

                     Class: 1 Class: 2 Class: 3
Sensitivity            0.9995  0.95936   0.9322
Specificity            0.9634  0.98684   0.9990
Pos Pred Value         0.9683  0.87167   0.9982
Neg Pred Value         0.9994  0.99618   0.9590
Prevalence             0.5280  0.08524   0.3868
Detection Rate         0.5277  0.08178   0.3606
Detection Prevalence   0.5450  0.09382   0.3612
Balanced Accuracy      0.9815  0.97310   0.9656

Random forest without cross validation and feature selection

dataForRandomForest = dataNew
trainIndex <- sample(nrow(dataForRandomForest), split*nrow(dataForRandomForest), replace = FALSE)
data_train <- dataForRandomForest[ trainIndex,]
data_test <- dataForRandomForest[-trainIndex,]
modelRFfun = randomForest(classLabel ~ .,data_train)
predictions <- predict(modelRFfun, data_test)
confusionMatrix(predictions, data_test$classLabel)

Confusion Matrix and Statistics

          Reference
Prediction     1     2     3
         1 53738     0     0
         2     0  8745     3
         3     0     0 39427

Overall Statistics
                                     
               Accuracy : 1          
                 95% CI : (0.9999, 1)
    No Information Rate : 0.5273     
    P-Value [Acc > NIR] : < 2.2e-16  
                                     
                  Kappa : 0.9999     
                                     
 Mcnemar's Test P-Value : NA         

Statistics by Class:

                     Class: 1 Class: 2 Class: 3
Sensitivity            1.0000  1.00000   0.9999
Specificity            1.0000  0.99997   1.0000
Pos Pred Value         1.0000  0.99966   1.0000
Neg Pred Value         1.0000  1.00000   1.0000
Prevalence             0.5273  0.08581   0.3869
Detection Rate         0.5273  0.08581   0.3869
Detection Prevalence   0.5273  0.08584   0.3869
Balanced Accuracy      1.0000  0.99998   1.0000

Clustering with k=7

datawith7 <- data
set.seed(12345)
#calculated clustering solution with optimal value k=7
k<-kmeans(datawith7[,3:5],centers = 7, iter.max = 20, nstart = 1)
k$centers

    Rating  Reviews Installs
1 4.932226 1.000116 1.000130
2 3.994163 1.000440 1.001571
3 4.317184 1.001328 1.002738
4 2.959759 1.000043 1.000281
5 4.602861 1.001345 1.001711
6 1.712746 1.000010 1.000080
7 3.562987 1.000111 1.000610

clusterTable<-table(k$cluster)
datawith7$classLabel = k$cluster
datawith7$classLabel <- as.factor(datawith7$classLabel)
clusterTable


    1     2     3     4     5     6     7 
42362 42247 63313 12003 67741  3535 23580

Plot clusters

plotcluster(datawith7[,3:5], k$cluster)

Naive bayes with 7 clusters as class labels without CV and feature selection

dataForNaiveBayesFor7 <- datawith7
set.seed(123)
trainIndex <- sample(nrow(dataForNaiveBayesFor7), split*nrow(dataForNaiveBayesFor7), replace = FALSE)
data_train <- na.omit(dataForNaiveBayesFor7[ trainIndex,])
data_test <- na.omit(dataForNaiveBayesFor7[-trainIndex,])
#Latest.updated and Latest.version has been removed, library limitation
modelNBfunFor7 = naiveBayes(classLabel ~ ., data_train)
predictionNB = predict(modelNBfunFor7, data_test)
confusionMatrix(predictionNB, data_test$classLabel)

Confusion Matrix and Statistics

          Reference
Prediction     1     2     3     4     5     6     7
         1 17056     3    20     0  6165     7     0
         2     0 10980  4047     9     0     0    78
         3     0   151 20465     0  2263     0     2
         4     0     6     0  3961     0    14   683
         5    63     0   493     0 18653     0     0
         6     5     1    12   741     7  1386     2
         7     0  5843    45    77     0     0  8675

Overall Statistics
                                        
               Accuracy : 0.7965        
                 95% CI : (0.794, 0.799)
    No Information Rate : 0.2658        
    P-Value [Acc > NIR] : < 2.2e-16     
                                        
                  Kappa : 0.7506        
                                        
 Mcnemar's Test P-Value : NA            

Statistics by Class:

                     Class: 1 Class: 2 Class: 3 Class: 4 Class: 5 Class: 6 Class: 7
Sensitivity            0.9960   0.6465   0.8159  0.82728   0.6886  0.98507  0.91896
Specificity            0.9269   0.9513   0.9686  0.99276   0.9926  0.99236  0.93549
Pos Pred Value         0.7336   0.7265   0.8944  0.84927   0.9711  0.64345  0.59255
Neg Pred Value         0.9991   0.9308   0.9416  0.99150   0.8980  0.99979  0.99123
Prevalence             0.1680   0.1667   0.2461  0.04698   0.2658  0.01381  0.09263
Detection Rate         0.1674   0.1077   0.2008  0.03887   0.1830  0.01360  0.08512
Detection Prevalence   0.2281   0.1483   0.2245  0.04576   0.1885  0.02114  0.14365
Balanced Accuracy      0.9615   0.7989   0.8922  0.91002   0.8406  0.98872  0.92723

Naive bayes with cross validation for 7 cluster value

#application name, (1st), Latest.updated(9th) and Latest.version(10th) has been removed, library limitation
col <-c(2,3,4,5,6,7,8,11,12)
x<-data_train[,col]
y<-data_train$classLabel
modelNBF7 = train(x,y,'nb',trControl=trainControl(method='cv',number=10))

Numerical 0 probability for all classes with observation 94Numerical 0 probability for all classes with observation 201Numerical 0 probability for all classes with observation 205Numerical 0 probability for all classes with observation 408Numerical 0 probability for all classes with observation 486Numerical 0 probability for all classes with observation 613Numerical 0 probability for all classes with observation 718Numerical 0 probability for all classes with observation 739Numerical 0 probability for all classes with observation 756Numerical 0 probability for all classes with observation 901Numerical 0 probability for all classes with observation 987Numerical 0 probability for all classes with observation 1104Numerical 0 probability for all classes with observation 1192Numerical 0 probability for all classes with observation 1211Numerical 0 probability for all classes with observation 1281Numerical 0 probability for all classes with observation 1522Numerical 0 probability for all classes with observation 1764Numerical 0 probability for all classes with observation 1808Numerical 0 probability for all classes with observation 1943Numerical 0 probability for all classes with observation 2305Numerical 0 probability for all classes with observation 2464Numerical 0 probability for all classes with observation 2781Numerical 0 probability for all classes with observation 2792Numerical 0 probability for all classes with observation 3071Numerical 0 probability for all classes with observation 3140Numerical 0 probability for all classes with observation 3160Numerical 0 probability for all classes with observation 3258Numerical 0 probability for all classes with observation 3376Numerical 0 probability for all classes with observation 3377Numerical 0 probability for all classes with observation 3454Numerical 0 probability for all classes with observation 3579Numerical 0 probability for all classes with observation 3593Numerical 0 probability for all classes with observation 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probability for all classes with observation 6160Numerical 0 probability for all classes with observation 6354Numerical 0 probability for all classes with observation 6551Numerical 0 probability for all classes with observation 6666Numerical 0 probability for all classes with observation 6766Numerical 0 probability for all classes with observation 7002Numerical 0 probability for all classes with observation 7044Numerical 0 probability for all classes with observation 7235Numerical 0 probability for all classes with observation 7517Numerical 0 probability for all classes with observation 7649Numerical 0 probability for all classes with observation 7673Numerical 0 probability for all classes with observation 7705Numerical 0 probability for all classes with observation 7806Numerical 0 probability for all classes with observation 7809Numerical 0 probability for all classes with observation 8236Numerical 0 probability for all classes with observation 8685Numerical 0 probability for all classes with observation 8755Numerical 0 probability for all classes with observation 8856Numerical 0 probability for all classes with observation 8860Numerical 0 probability for all classes with observation 9248Numerical 0 probability for all classes with observation 9524Numerical 0 probability for all classes with observation 9645Numerical 0 probability for all classes with observation 9872Numerical 0 probability for all classes with observation 9943Numerical 0 probability for all classes with observation 10116Numerical 0 probability for all classes with observation 10151Numerical 0 probability for all classes with observation 10519Numerical 0 probability for all classes with observation 10676Numerical 0 probability for all classes with observation 10984Numerical 0 probability for all classes with observation 11070Numerical 0 probability for all classes with observation 11123Numerical 0 probability for all classes with observation 11168Numerical 0 probability for all classes with observation 11317Numerical 0 probability for all classes with observation 11318Numerical 0 probability for all classes with observation 11421Numerical 0 probability for all classes with observation 11542Numerical 0 probability for all classes with observation 11714Numerical 0 probability for all classes with observation 11745Numerical 0 probability for all classes with observation 11798Numerical 0 probability for all classes with observation 11900Numerical 0 probability for all classes with observation 11955Numerical 0 probability for all classes with observation 12038Numerical 0 probability for all classes with observation 12091Numerical 0 probability for all classes with observation 12215Numerical 0 probability for all classes with observation 12268Numerical 0 probability for all classes with observation 12280Numerical 0 probability for all classes with observation 12294Numerical 0 probability for all classes with observation 12468Numerical 0 probability for all classes with observation 12551Numerical 0 probability for all classes with observation 12603Numerical 0 probability for all classes with observation 12618Numerical 0 probability for all classes with observation 12631Numerical 0 probability for all classes with observation 12690Numerical 0 probability for all classes with observation 12867Numerical 0 probability for all classes with observation 13091Numerical 0 probability for all classes with observation 13289Numerical 0 probability for all classes with observation 13300Numerical 0 probability for all classes with observation 13366Numerical 0 probability for all classes with observation 13434Numerical 0 probability for all classes with observation 13571Numerical 0 probability for all classes with observation 13611Numerical 0 probability for all classes with observation 13643Numerical 0 probability for all classes with observation 13731Numerical 0 probability for all classes with observation 13749Numerical 0 probability for all classes with observation 13796Numerical 0 probability for all classes with observation 14621Numerical 0 probability for all classes with observation 14713Numerical 0 probability for all classes with observation 14738Numerical 0 probability for all classes with observation 14740Numerical 0 probability for all classes with observation 14971Numerical 0 probability for all classes with observation 15028Numerical 0 probability for all classes with observation 15044Numerical 0 probability for all classes with observation 15082Numerical 0 probability for all classes with observation 68Numerical 0 probability for all classes with observation 133Numerical 0 probability for all classes with observation 285Numerical 0 probability for all classes with observation 299Numerical 0 probability for all classes with observation 367Numerical 0 probability for all classes with observation 486Numerical 0 probability for all classes with observation 551Numerical 0 probability for all classes with observation 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all classes with observation 1839Numerical 0 probability for all classes with observation 1862Numerical 0 probability for all classes with observation 2103Numerical 0 probability for all classes with observation 2372Numerical 0 probability for all classes with observation 2483Numerical 0 probability for all classes with observation 2722Numerical 0 probability for all classes with observation 2749Numerical 0 probability for all classes with observation 3079Numerical 0 probability for all classes with observation 3329Numerical 0 probability for all classes with observation 3386Numerical 0 probability for all classes with observation 3459Numerical 0 probability for all classes with observation 3524Numerical 0 probability for all classes with observation 3539Numerical 0 probability for all classes with observation 3616Numerical 0 probability for all classes with observation 3759Numerical 0 probability for all classes with observation 3771Numerical 0 probability for all classes with observation 3788Numerical 0 probability for all classes with observation 3892Numerical 0 probability for all classes with observation 3990Numerical 0 probability for all classes with observation 4026Numerical 0 probability for all classes with observation 4074Numerical 0 probability for all classes with observation 4214Numerical 0 probability for all classes with observation 4353Numerical 0 probability for all classes with observation 4487Numerical 0 probability for all classes with observation 4490Numerical 0 probability for all classes with observation 4575Numerical 0 probability for all classes with observation 4772Numerical 0 probability for all classes with observation 4874Numerical 0 probability for all classes with observation 4886Numerical 0 probability for all classes with observation 4905Numerical 0 probability for all classes with observation 5135Numerical 0 probability for all classes with observation 5763Numerical 0 probability for all classes with observation 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probability for all classes with observation 8054Numerical 0 probability for all classes with observation 8207Numerical 0 probability for all classes with observation 8215Numerical 0 probability for all classes with observation 8381Numerical 0 probability for all classes with observation 8409Numerical 0 probability for all classes with observation 8627Numerical 0 probability for all classes with observation 8651Numerical 0 probability for all classes with observation 8695Numerical 0 probability for all classes with observation 8717Numerical 0 probability for all classes with observation 8800Numerical 0 probability for all classes with observation 8832Numerical 0 probability for all classes with observation 9003Numerical 0 probability for all classes with observation 9080Numerical 0 probability for all classes with observation 9187Numerical 0 probability for all classes with observation 9474Numerical 0 probability for all classes with observation 9575Numerical 0 probability for all classes with observation 9993Numerical 0 probability for all classes with observation 10032Numerical 0 probability for all classes with observation 10105Numerical 0 probability for all classes with observation 10189Numerical 0 probability for all classes with observation 10719Numerical 0 probability for all classes with observation 10782Numerical 0 probability for all classes with observation 10823Numerical 0 probability for all classes with observation 11060Numerical 0 probability for all classes with observation 11425Numerical 0 probability for all classes with observation 11540Numerical 0 probability for all classes with observation 11605Numerical 0 probability for all classes with observation 11610Numerical 0 probability for all classes with observation 11659Numerical 0 probability for all classes with observation 11778Numerical 0 probability for all classes with observation 11787Numerical 0 probability for all classes with observation 11843Numerical 0 probability for all classes with observation 11925Numerical 0 probability for all classes with observation 12278Numerical 0 probability for all classes with observation 12484Numerical 0 probability for all classes with observation 12573Numerical 0 probability for all classes with observation 12642Numerical 0 probability for all classes with observation 12722Numerical 0 probability for all classes with observation 12822Numerical 0 probability for all classes with observation 12880Numerical 0 probability for all classes with observation 12883Numerical 0 probability for all classes with observation 12997Numerical 0 probability for all classes with observation 13033Numerical 0 probability for all classes with observation 13101Numerical 0 probability for all classes with observation 13164Numerical 0 probability for all classes with observation 13260Numerical 0 probability for all classes with observation 13275Numerical 0 probability for all classes with observation 13428Numerical 0 probability for all classes with observation 13784Numerical 0 probability for all classes with observation 13787Numerical 0 probability for all classes with observation 13876Numerical 0 probability for all classes with observation 14022Numerical 0 probability for all classes with observation 14201Numerical 0 probability for all classes with observation 14264Numerical 0 probability for all classes with observation 14306Numerical 0 probability for all classes with observation 14324Numerical 0 probability for all classes with observation 14522Numerical 0 probability for all classes with observation 14637Numerical 0 probability for all classes with observation 14794Numerical 0 probability for all classes with observation 15027Numerical 0 probability for all classes with observation 15156Numerical 0 probability for all classes with observation 15170Numerical 0 probability for all classes with observation 13Numerical 0 probability for all classes with observation 341Numerical 0 probability for all classes with observation 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all classes with observation 2061Numerical 0 probability for all classes with observation 2098Numerical 0 probability for all classes with observation 2224Numerical 0 probability for all classes with observation 2322Numerical 0 probability for all classes with observation 2917Numerical 0 probability for all classes with observation 3028Numerical 0 probability for all classes with observation 3322Numerical 0 probability for all classes with observation 3376Numerical 0 probability for all classes with observation 3424Numerical 0 probability for all classes with observation 3445Numerical 0 probability for all classes with observation 3781Numerical 0 probability for all classes with observation 3821Numerical 0 probability for all classes with observation 4017Numerical 0 probability for all classes with observation 4372Numerical 0 probability for all classes with observation 4810Numerical 0 probability for all classes with observation 4841Numerical 0 probability for all classes with observation 4925Numerical 0 probability for all classes with observation 5096Numerical 0 probability for all classes with observation 5130Numerical 0 probability for all classes with observation 5193Numerical 0 probability for all classes with observation 5234Numerical 0 probability for all classes with observation 5248Numerical 0 probability for all classes with observation 5290Numerical 0 probability for all classes with observation 5404Numerical 0 probability for all classes with observation 5444Numerical 0 probability for all classes with observation 5665Numerical 0 probability for all classes with observation 6087Numerical 0 probability for all classes with observation 6156Numerical 0 probability for all classes with observation 6211Numerical 0 probability for all classes with observation 6350Numerical 0 probability for all classes with observation 6559Numerical 0 probability for all classes with observation 6640Numerical 0 probability for all classes with observation 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probability for all classes with observation 8657Numerical 0 probability for all classes with observation 8706Numerical 0 probability for all classes with observation 8938Numerical 0 probability for all classes with observation 9352Numerical 0 probability for all classes with observation 9353Numerical 0 probability for all classes with observation 9395Numerical 0 probability for all classes with observation 9518Numerical 0 probability for all classes with observation 9568Numerical 0 probability for all classes with observation 9829Numerical 0 probability for all classes with observation 10335Numerical 0 probability for all classes with observation 10344Numerical 0 probability for all classes with observation 10426Numerical 0 probability for all classes with observation 10647Numerical 0 probability for all classes with observation 10650Numerical 0 probability for all classes with observation 10681Numerical 0 probability for all classes with observation 10934Numerical 0 probability for all classes with observation 10941Numerical 0 probability for all classes with observation 11294Numerical 0 probability for all classes with observation 11379Numerical 0 probability for all classes with observation 11458Numerical 0 probability for all classes with observation 11674Numerical 0 probability for all classes with observation 11815Numerical 0 probability for all classes with observation 11881Numerical 0 probability for all classes with observation 12218Numerical 0 probability for all classes with observation 12269Numerical 0 probability for all classes with observation 12374Numerical 0 probability for all classes with observation 12381Numerical 0 probability for all classes with observation 12531Numerical 0 probability for all classes with observation 12688Numerical 0 probability for all classes with observation 12769Numerical 0 probability for all classes with observation 12946Numerical 0 probability for all classes with observation 13118Numerical 0 probability for all classes with observation 13167Numerical 0 probability for all classes with observation 13196Numerical 0 probability for all classes with observation 13346Numerical 0 probability for all classes with observation 13484Numerical 0 probability for all classes with observation 13538Numerical 0 probability for all classes with observation 13681Numerical 0 probability for all classes with observation 13777Numerical 0 probability for all classes with observation 14273Numerical 0 probability for all classes with observation 14695Numerical 0 probability for all classes with observation 14785Numerical 0 probability for all classes with observation 14861Numerical 0 probability for all classes with observation 14916Numerical 0 probability for all classes with observation 14949Numerical 0 probability for all classes with observation 14970Numerical 0 probability for all classes with observation 15112Numerical 0 probability for all classes with observation 15264Numerical 0 probability for all classes with observation 8Numerical 0 probability for all classes with observation 44Numerical 0 probability for all classes with observation 146Numerical 0 probability for all classes with observation 389Numerical 0 probability for all classes with observation 494Numerical 0 probability for all classes with observation 646Numerical 0 probability for all classes with observation 1070Numerical 0 probability for all classes with observation 1088Numerical 0 probability for all classes with observation 1148Numerical 0 probability for all classes with observation 1434Numerical 0 probability for all classes with observation 1534Numerical 0 probability for all classes with observation 1571Numerical 0 probability for all classes with observation 1652Numerical 0 probability for all classes with observation 1693Numerical 0 probability for all classes with observation 1762Numerical 0 probability for all classes with observation 1959Numerical 0 probability for all classes with observation 2081Numerical 0 probability for all classes with observation 2262Numerical 0 probability for all classes with observation 2281Numerical 0 probability for all classes with observation 2345Numerical 0 probability for all classes with observation 2347Numerical 0 probability for all classes with observation 2359Numerical 0 probability for all classes with observation 2661Numerical 0 probability for all classes with observation 3079Numerical 0 probability for all classes with observation 3134Numerical 0 probability for all classes with observation 3219Numerical 0 probability for all classes with observation 3260Numerical 0 probability for all classes with observation 3293Numerical 0 probability for all classes with observation 3397Numerical 0 probability for all classes with observation 3590Numerical 0 probability for all classes with observation 3665Numerical 0 probability for all classes with observation 3680Numerical 0 probability for all classes with observation 3701Numerical 0 probability for all classes with observation 4006Numerical 0 probability for all classes with observation 4287Numerical 0 probability for all classes with observation 4328Numerical 0 probability for all classes with observation 4538Numerical 0 probability for all classes with observation 4699Numerical 0 probability for all classes with observation 4785Numerical 0 probability for all classes with observation 5503Numerical 0 probability for all classes with observation 5609Numerical 0 probability for all classes with observation 5667Numerical 0 probability for all classes with observation 5817Numerical 0 probability for all classes with observation 5964Numerical 0 probability for all classes with observation 6114Numerical 0 probability for all classes with observation 6177Numerical 0 probability for all classes with observation 6205Numerical 0 probability for all classes with observation 6291Numerical 0 probability for all classes with observation 6347Numerical 0 probability for all classes with observation 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probability for all classes with observation 8599Numerical 0 probability for all classes with observation 8663Numerical 0 probability for all classes with observation 8684Numerical 0 probability for all classes with observation 8707Numerical 0 probability for all classes with observation 8899Numerical 0 probability for all classes with observation 9122Numerical 0 probability for all classes with observation 9379Numerical 0 probability for all classes with observation 9398Numerical 0 probability for all classes with observation 9427Numerical 0 probability for all classes with observation 9547Numerical 0 probability for all classes with observation 9552Numerical 0 probability for all classes with observation 9583Numerical 0 probability for all classes with observation 9654Numerical 0 probability for all classes with observation 9666Numerical 0 probability for all classes with observation 9749Numerical 0 probability for all classes with observation 9789Numerical 0 probability for all 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with observation 11358Numerical 0 probability for all classes with observation 11379Numerical 0 probability for all classes with observation 11449Numerical 0 probability for all classes with observation 11487Numerical 0 probability for all classes with observation 11497Numerical 0 probability for all classes with observation 11519Numerical 0 probability for all classes with observation 11545Numerical 0 probability for all classes with observation 11757Numerical 0 probability for all classes with observation 11999Numerical 0 probability for all classes with observation 12246Numerical 0 probability for all classes with observation 12428Numerical 0 probability for all classes with observation 12932Numerical 0 probability for all classes with observation 12935Numerical 0 probability for all classes with observation 12976Numerical 0 probability for all classes with observation 13227Numerical 0 probability for all classes with observation 13287Numerical 0 probability for all classes with observation 13361Numerical 0 probability for all classes with observation 13371Numerical 0 probability for all classes with observation 13381Numerical 0 probability for all classes with observation 13387Numerical 0 probability for all classes with observation 13388Numerical 0 probability for all classes with observation 13398Numerical 0 probability for all classes with observation 13436Numerical 0 probability for all classes with observation 13479Numerical 0 probability for all classes with observation 13587Numerical 0 probability for all classes with observation 13729Numerical 0 probability for all classes with observation 13808Numerical 0 probability for all classes with observation 13860Numerical 0 probability for all classes with observation 13943Numerical 0 probability for all classes with observation 14241Numerical 0 probability for all classes with observation 14258Numerical 0 probability for all classes with observation 14324Numerical 0 probability for all classes with observation 14330Numerical 0 probability for all classes with observation 14357Numerical 0 probability for all classes with observation 14456Numerical 0 probability for all classes with observation 14571Numerical 0 probability for all classes with observation 14593Numerical 0 probability for all classes with observation 14785Numerical 0 probability for all classes with observation 14872Numerical 0 probability for all classes with observation 14972Numerical 0 probability for all classes with observation 15065Numerical 0 probability for all classes with observation 15205Numerical 0 probability for all classes with observation 64Numerical 0 probability for all classes with observation 504Numerical 0 probability for all classes with observation 631Numerical 0 probability for all classes with observation 641Numerical 0 probability for all classes with observation 673Numerical 0 probability for all classes with observation 679Numerical 0 probability for all classes with observation 726Numerical 0 probability for all classes with observation 732Numerical 0 probability for all classes with observation 1060Numerical 0 probability for all classes with observation 1162Numerical 0 probability for all classes with observation 1164Numerical 0 probability for all classes with observation 1422Numerical 0 probability for all classes with observation 1509Numerical 0 probability for all classes with observation 1510Numerical 0 probability for all classes with observation 1616Numerical 0 probability for all classes with observation 1808Numerical 0 probability for all classes with observation 1858Numerical 0 probability for all classes with observation 1890Numerical 0 probability for all classes with observation 2073Numerical 0 probability for all classes with observation 2111Numerical 0 probability for all classes with observation 2162Numerical 0 probability for all classes with observation 2235Numerical 0 probability for all classes with observation 2608Numerical 0 probability for all classes with observation 2697Numerical 0 probability for all classes with observation 2736Numerical 0 probability for all classes with observation 2751Numerical 0 probability for all classes with observation 2765Numerical 0 probability for all classes with observation 2840Numerical 0 probability for all classes with observation 3088Numerical 0 probability for all classes with observation 3123Numerical 0 probability for all classes with observation 3351Numerical 0 probability for all classes with observation 3452Numerical 0 probability for all classes with observation 3467Numerical 0 probability for all classes with observation 3469Numerical 0 probability for all classes with observation 3606Numerical 0 probability for all classes with observation 3632Numerical 0 probability for all classes with observation 3709Numerical 0 probability for all classes with observation 3816Numerical 0 probability for all classes with observation 4165Numerical 0 probability for all classes with observation 4230Numerical 0 probability for all classes with observation 4651Numerical 0 probability for all classes with observation 4850Numerical 0 probability for all classes with observation 4984Numerical 0 probability for all classes with observation 5057Numerical 0 probability for all classes with observation 5175Numerical 0 probability for all classes with observation 5247Numerical 0 probability for all classes with observation 5330Numerical 0 probability for all classes with observation 5491Numerical 0 probability for all classes with observation 5499Numerical 0 probability for all classes with observation 5674Numerical 0 probability for all classes with observation 5711Numerical 0 probability for all classes with observation 6042Numerical 0 probability for all classes with observation 6137Numerical 0 probability for all classes with observation 6295Numerical 0 probability for all classes with observation 6531Numerical 0 probability for all classes with observation 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probability for all classes with observation 8902Numerical 0 probability for all classes with observation 8969Numerical 0 probability for all classes with observation 9011Numerical 0 probability for all classes with observation 9099Numerical 0 probability for all classes with observation 9109Numerical 0 probability for all classes with observation 9147Numerical 0 probability for all classes with observation 9190Numerical 0 probability for all classes with observation 9262Numerical 0 probability for all classes with observation 9624Numerical 0 probability for all classes with observation 9652Numerical 0 probability for all classes with observation 9683Numerical 0 probability for all classes with observation 9901Numerical 0 probability for all classes with observation 10037Numerical 0 probability for all classes with observation 10112Numerical 0 probability for all classes with observation 10249Numerical 0 probability for all classes with observation 10265Numerical 0 probability for all 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with observation 12145Numerical 0 probability for all classes with observation 12250Numerical 0 probability for all classes with observation 12438Numerical 0 probability for all classes with observation 12530Numerical 0 probability for all classes with observation 12584Numerical 0 probability for all classes with observation 12850Numerical 0 probability for all classes with observation 12947Numerical 0 probability for all classes with observation 13108Numerical 0 probability for all classes with observation 13350Numerical 0 probability for all classes with observation 13377Numerical 0 probability for all classes with observation 13384Numerical 0 probability for all classes with observation 13474Numerical 0 probability for all classes with observation 13582Numerical 0 probability for all classes with observation 13689Numerical 0 probability for all classes with observation 13846Numerical 0 probability for all classes with observation 13893Numerical 0 probability for all classes with observation 13941Numerical 0 probability for all classes with observation 14022Numerical 0 probability for all classes with observation 14062Numerical 0 probability for all classes with observation 14372Numerical 0 probability for all classes with observation 14400Numerical 0 probability for all classes with observation 14463Numerical 0 probability for all classes with observation 14652Numerical 0 probability for all classes with observation 14842Numerical 0 probability for all classes with observation 15185Numerical 0 probability for all classes with observation 15268Numerical 0 probability for all classes with observation 131Numerical 0 probability for all classes with observation 437Numerical 0 probability for all classes with observation 443Numerical 0 probability for all classes with observation 621Numerical 0 probability for all classes with observation 895Numerical 0 probability for all classes with observation 913Numerical 0 probability for all classes with observation 963Numerical 0 probability for all classes with observation 1090Numerical 0 probability for all classes with observation 1268Numerical 0 probability for all classes with observation 1425Numerical 0 probability for all classes with observation 1456Numerical 0 probability for all classes with observation 1698Numerical 0 probability for all classes with observation 1992Numerical 0 probability for all classes with observation 2159Numerical 0 probability for all classes with observation 2182Numerical 0 probability for all classes with observation 2392Numerical 0 probability for all classes with observation 2404Numerical 0 probability for all classes with observation 2739Numerical 0 probability for all classes with observation 2791Numerical 0 probability for all classes with observation 3202Numerical 0 probability for all classes with observation 3301Numerical 0 probability for all classes with observation 3357Numerical 0 probability for all classes with observation 3389Numerical 0 probability for all classes with observation 3490Numerical 0 probability for all classes with observation 3517Numerical 0 probability for all classes with observation 3847Numerical 0 probability for all classes with observation 3904Numerical 0 probability for all classes with observation 3969Numerical 0 probability for all classes with observation 4121Numerical 0 probability for all classes with observation 4136Numerical 0 probability for all classes with observation 4144Numerical 0 probability for all classes with observation 4197Numerical 0 probability for all classes with observation 4295Numerical 0 probability for all classes with observation 4399Numerical 0 probability for all classes with observation 4447Numerical 0 probability for all classes with observation 4634Numerical 0 probability for all classes with observation 4817Numerical 0 probability for all classes with observation 4959Numerical 0 probability for all classes with observation 5038Numerical 0 probability for all classes with observation 5323Numerical 0 probability for all classes with observation 5335Numerical 0 probability for all classes with observation 5336Numerical 0 probability for all classes with observation 5457Numerical 0 probability for all classes with observation 5562Numerical 0 probability for all classes with observation 5646Numerical 0 probability for all classes with observation 5681Numerical 0 probability for all classes with observation 5690Numerical 0 probability for all classes with observation 5780Numerical 0 probability for all classes with observation 5828Numerical 0 probability for all classes with observation 5871Numerical 0 probability for all classes with observation 5883Numerical 0 probability for all classes with observation 5955Numerical 0 probability for all classes with observation 6286Numerical 0 probability for all classes with observation 6303Numerical 0 probability for all classes with observation 6346Numerical 0 probability for all classes with observation 6547Numerical 0 probability for all classes with observation 6591Numerical 0 probability for all classes with observation 6630Numerical 0 probability for all classes with observation 6791Numerical 0 probability for all classes with observation 6890Numerical 0 probability for all classes with observation 7098Numerical 0 probability for all classes with observation 7168Numerical 0 probability for all classes with observation 7192Numerical 0 probability for all classes with observation 7321Numerical 0 probability for all classes with observation 7357Numerical 0 probability for all classes with observation 7427Numerical 0 probability for all classes with observation 7549Numerical 0 probability for all classes with observation 7550Numerical 0 probability for all classes with observation 7692Numerical 0 probability for all classes with observation 7743Numerical 0 probability for all classes with observation 7781Numerical 0 probability for all classes with observation 7806Numerical 0 probability for all classes with observation 7824Numerical 0 probability for all classes with observation 7874Numerical 0 probability for all classes with observation 7876Numerical 0 probability for all classes with observation 7959Numerical 0 probability for all classes with observation 7990Numerical 0 probability for all classes with observation 8183Numerical 0 probability for all classes with observation 8218Numerical 0 probability for all classes with observation 8284Numerical 0 probability for all classes with observation 8535Numerical 0 probability for all classes with observation 8739Numerical 0 probability for all classes with observation 8816Numerical 0 probability for all classes with observation 8868Numerical 0 probability for all classes with observation 8873Numerical 0 probability for all classes with observation 8912Numerical 0 probability for all classes with observation 9296Numerical 0 probability for all classes with observation 9315Numerical 0 probability for all classes with observation 9618Numerical 0 probability for all classes with observation 9699Numerical 0 probability for all classes with observation 9963Numerical 0 probability for all classes with observation 10061Numerical 0 probability for all classes with observation 10220Numerical 0 probability for all classes with observation 10403Numerical 0 probability for all classes with observation 10667Numerical 0 probability for all classes with observation 10740Numerical 0 probability for all classes with observation 10841Numerical 0 probability for all classes with observation 10967Numerical 0 probability for all classes with observation 11026Numerical 0 probability for all classes with observation 11109Numerical 0 probability for all classes with observation 11261Numerical 0 probability for all classes with observation 11658Numerical 0 probability for all classes with observation 12096Numerical 0 probability for all classes with observation 12306Numerical 0 probability for all classes with observation 12844Numerical 0 probability for all classes with observation 12848Numerical 0 probability for all classes with observation 13056Numerical 0 probability for all classes with observation 13164Numerical 0 probability for all classes with observation 13194Numerical 0 probability for all classes with observation 13472Numerical 0 probability for all classes with observation 13618Numerical 0 probability for all classes with observation 13769Numerical 0 probability for all classes with observation 13993Numerical 0 probability for all classes with observation 14010Numerical 0 probability for all classes with observation 14253Numerical 0 probability for all classes with observation 14382Numerical 0 probability for all classes with observation 14395Numerical 0 probability for all classes with observation 14502Numerical 0 probability for all classes with observation 14592Numerical 0 probability for all classes with observation 14605Numerical 0 probability for all classes with observation 14706Numerical 0 probability for all classes with observation 14729Numerical 0 probability for all classes with observation 14996Numerical 0 probability for all classes with observation 15184Numerical 0 probability for all classes with observation 15198Numerical 0 probability for all classes with observation 15233

Random forest for 7clusters

#9th column(Last.updated) can be added again, as date format works in random forest.
columns = c(2,3,4,5,6,8,9,11,12,13)
dataForRandomForestFor7 = datawith7[,columns]
trainIndex <- sample(nrow(dataForRandomForestFor7), split*nrow(dataForRandomForestFor7), replace = FALSE)
data_train <- dataForRandomForestFor7[ trainIndex,]
data_test <- dataForRandomForestFor7[-trainIndex,]
modelRFfun = randomForest(classLabel ~ .,data_train)
predictions <- predict(modelRFfun, data_test)
confusionMatrix(predictions, data_test$classLabel)

Confusion Matrix and Statistics

          Reference
Prediction     1     2     3     4     5     6     7
         1 16886     0     0     0     0     0     0
         2     0 17028     1     0     0     0     0
         3     0     0 25465     0     2     0     0
         4     0     0     0  4764     0     2     1
         5     0     0     1     0 26962     0     0
         6     0     0     0     0     0  1423     0
         7     0     0     0     0     0     0  9378

Overall Statistics
                                     
               Accuracy : 0.9999     
                 95% CI : (0.9999, 1)
    No Information Rate : 0.2646     
    P-Value [Acc > NIR] : < 2.2e-16  
                                     
                  Kappa : 0.9999     
                                     
 Mcnemar's Test P-Value : NA         

Statistics by Class:

                     Class: 1 Class: 2 Class: 3 Class: 4 Class: 5 Class: 6 Class: 7
Sensitivity            1.0000   1.0000   0.9999  1.00000   0.9999  0.99860  0.99989
Specificity            1.0000   1.0000   1.0000  0.99997   1.0000  1.00000  1.00000
Pos Pred Value         1.0000   0.9999   0.9999  0.99937   1.0000  1.00000  1.00000
Neg Pred Value         1.0000   1.0000   1.0000  1.00000   1.0000  0.99998  0.99999
Prevalence             0.1657   0.1671   0.2499  0.04675   0.2646  0.01398  0.09203
Detection Rate         0.1657   0.1671   0.2499  0.04675   0.2646  0.01396  0.09202
Detection Prevalence   0.1657   0.1671   0.2499  0.04678   0.2646  0.01396  0.09202
Balanced Accuracy      1.0000   1.0000   0.9999  0.99998   1.0000  0.99930  0.99995

K nearest neighbor

#KNN requires all numeric features, hence all important features have been considered for this algorithm.
dataForKNNFor7 = datawith7
dataForKNNFor7$Category = as.numeric(dataForKNNFor7$Category)
columns <- c(2,3,4,5,6,13)
dataForKNNFor7 = dataForKNNFor7[,columns]
trainIndex <- sample(nrow(dataForKNNFor7), split*nrow(dataForKNNFor7), replace = FALSE)
data_train <- na.omit(dataForKNNFor7[ trainIndex,])
data_test <- dataForKNNFor7[-trainIndex,]
predictions = knn(data_train, data_test,cl=data_train$classLabel,k=11)
confusionMatrix(predictions, data_test$classLabel)

Confusion Matrix and Statistics

          Reference
Prediction     1     2     3     4     5     6     7
         1 16781    40     0     0     0     0     0
         2   253 16582    86     2     1     0     0
         3    44   328 25297   366    13     0     2
         4     0     0     0  4342     0     8     0
         5     1     0    21    49 26999    13   154
         6     0     0     0     0     0  1130     0
         7     0     0     0     2     0   223  9176

Overall Statistics
                                         
               Accuracy : 0.9842         
                 95% CI : (0.9835, 0.985)
    No Information Rate : 0.2651         
    P-Value [Acc > NIR] : < 2.2e-16      
                                         
                  Kappa : 0.9803         
                                         
 Mcnemar's Test P-Value : NA             

Statistics by Class:

                     Class: 1 Class: 2 Class: 3 Class: 4 Class: 5 Class: 6 Class: 7
Sensitivity            0.9826   0.9783   0.9958  0.91199   0.9995  0.82242  0.98328
Specificity            0.9995   0.9960   0.9902  0.99992   0.9968  1.00000  0.99757
Pos Pred Value         0.9976   0.9798   0.9711  0.99816   0.9913  1.00000  0.97607
Neg Pred Value         0.9965   0.9957   0.9986  0.99571   0.9998  0.99758  0.99831
Prevalence             0.1676   0.1663   0.2493  0.04672   0.2651  0.01348  0.09157
Detection Rate         0.1647   0.1627   0.2482  0.04260   0.2649  0.01109  0.09004
Detection Prevalence   0.1651   0.1661   0.2556  0.04268   0.2673  0.01109  0.09225
Balanced Accuracy      0.9910   0.9871   0.9930  0.95596   0.9982  0.91121  0.99043

Popular categories with respect to number of installs

graphData <- data.clean
graphData %>%
  count(Category, Installs) %>%
  group_by(Category) %>%
  summarize(
    TotalInstalls = sum(as.numeric(Installs))
  ) %>%
  arrange(-TotalInstalls) %>%
  hchart('scatter', hcaes(x = "Category", y = "TotalInstalls", size = "TotalInstalls", color = "Category")) %>%
  hc_add_theme(hc_theme_538()) %>%
  hc_title(text = "Most popular categories (# of installs)")

Popular category with respect to average rating

graphData %>%
  count(Category, Rating) %>%
  group_by(Category) %>%
  summarize(
    Rating = mean(Rating)
  ) %>%
  arrange(-Rating) %>%
  hchart('scatter', hcaes(x = "Category", y = "Rating", size = "Rating", color = "Category")) %>%
  hc_add_theme(hc_theme_538()) %>%
  hc_title(text = "Categories with their mean rating")

Distribution of application size

graphData %>%
  count(Size) %>%
  hchart('area', hcaes(x = "Size", y = "n")) %>%
  hc_colors("#fb4901") %>%
  hc_add_theme(hc_theme_ffx()) %>%
  hc_title(text = "Distribution of application size (in MB)")

Number of applications for each installation category

tmp <- graphData %>%
  group_by(
    Installs.Group = cut(Installs, breaks= seq(0, 1000000000, by = 10000))
    ) %>% 
  summarise(
    n= n()
    )

Factor `Installs.Group` contains implicit NA, consider using `forcats::fct_explicit_na`

highchart() %>%
  hc_chart(
    type = "pie"
    ) %>%
  hc_add_series_labels_values(
    labels = tmp$Installs.Group, values = tmp$n
    ) %>%
  hc_title(
    text="Number of installs (groups per 10k)"
    ) %>%
  hc_add_theme(hc_theme_economist())

'hc_add_series_labels_values' is deprecated.
Use 'hc_add_series' instead.
See help("Deprecated")

Percentage of paid vs free applications

tmp <- graphData %>%
  count(Type) %>%
  mutate(perc = round((n /sum(n))*100)) %>%
  arrange(desc(perc))

    hciconarray(tmp$Type, tmp$perc, icons = "android", size = 5) %>%
  hc_title(text="Percentage of paid vs free apps")

Percentage of paid vs free applications per category

graphData %>% 
  group_by(Category, Type) %>%
  summarize(
    n = n()
  ) %>%
  mutate(perc = round((n /sum(n))*100)) %>%
  hchart('bar', hcaes(x = 'Category', y = 'perc', group = 'Type')) %>%
  hc_plotOptions(series=list(stacking='normal')) %>%
  hc_title(text="Percentage of Free vs Paid by Category") %>%
  hc_add_theme(hc_theme_flat())

Median price per category

graphData %>%
  filter(Type == 1) %>%
  group_by(Category) %>%
  summarize(
    Price = median(Price)
  ) %>%
  arrange(-Price) %>%
  hchart('treemap', hcaes(x = 'Category', value = 'Price', color = 'Price')) %>%
  hc_add_theme(hc_theme_elementary()) %>%
  hc_title(text="Median price per category")

Total revenue generated by each category

graphData %>%
  filter(Type == 1) %>%
  mutate(
    Total.Paid = Price * Installs
  ) %>%
  group_by(Category) %>%
  summarize(USD.Paid = sum(Total.Paid)) %>%
  arrange(-USD.Paid) %>%
  hchart('treemap', hcaes(x = 'Category', value = 'USD.Paid', color = 'USD.Paid')) %>%
  hc_add_theme(hc_theme_elementary()) %>%
  hc_title(text="Total amount spent by category (installs * price)")

Number of installation by audience

tmp <- graphData %>%
  group_by(Content.Rating) %>%
  summarize(Total.Installs = sum(Installs)) %>%
  arrange(-Total.Installs)
highchart() %>% 
  hc_chart(type ="column",
           options3d = list(enabled = TRUE, alpha = 15, beta = 15)) %>%
  hc_xAxis(categories = tmp$Content.Rating) %>% 
  hc_add_series(data = tmp$Total.Installs, name = "Total.Installs") %>%
  hc_add_theme(hc_theme_smpl()) %>%
  hc_title(
    text="Number of Installs by audience (all apps)"
    ) %>%
    hc_chart(
      borderColor = '#EBBA95',
      borderRadius = 10,
      borderWidth = 1,
      backgroundColor = list(
        linearGradient = c(0, 0, 500, 500), stops = list(
               list(0, 'rgb(255, 255, 255)'),
               list(1, 'rgb(180, 180, 255)')
             )))

number of applications by last updated date

tmp <- graphData %>% count(Last.Updated)

# Transform data into time series
time_series <- xts(
  tmp$n, order.by = tmp$Last.Updated 
)

highchart(type = "stock") %>% 
  hc_title(text = "Last updated date") %>% 
  hc_subtitle(text = "Number of applications by date of last update") %>% 
  hc_add_series(time_series) %>%
  hc_add_theme(hc_theme_gridlight())


rm(time_series)

Number of installation per Minimum android version with respect to application type

graphData %>%
 filter(Min.Android.Ver > 0, Type %in% c(0, 1)
   ) %>%
 group_by(as.factor(Min.Android.Ver), Type) %>%
 rename(Minimum.Android.Version = "as.factor(Min.Android.Ver)") %>%
 summarize(Total.Installs = sum(Installs)) %>%
 hchart(
   type = "heatmap", hcaes(x = Minimum.Android.Version, y = Type, value = Total.Installs)
   ) %>%
 hc_title(text = "Minimum Android Version (by number of installs)")

Top 10 applications

graphData %>%
    dplyr::select(App.Name, Installs, Category) %>%
    arrange(-Installs) %>%
    head(10)

---
title: "Google App store success prediction"
output:
  html_notebook: default
  pdf_document: default
  html_document: dafault
---

This is an [R Markdown](http://rmarkdown.rstudio.com) Notebook. When you execute code within the notebook, the results appear beneath the code. 

Try executing these chunks by clicking the *Run* button within the chunk or by placing your cursor inside it and pressing *Ctrl+Shift+Enter*. 


**Load packages**
```{r Load packages}
install.packages('tidyverse')
install.packages('highcharter')
install.packages('lubridate')
install.packages('stringr')
install.packages('xts')
install.packages('magrittr')
install.packages('deplyr')
install.packages('caretEnsemble')
install.packages('psych')
install.packages('Amelia')
install.packages('mice')
install.packages('GGally')
install.packages('rpart')
install.packages('normalr')
install.packages('cluster')
install.packages('HSAUR')
install.packages('fpc')
install.packages('e1071')
install.packages('klaR')
install.packages('caret')
install.packages('MASS')
install.packages('randomForest')
install.packages('class')
library(tidyverse)
library(highcharter) 
library(lubridate)
library(stringr)
library(xts)
library(magrittr)
library(dplyr)
library(caretEnsemble)
library(psych)
library(Amelia)
library(mice)
library(GGally)
library(rpart)
library(normalr)
library(cluster)
library(HSAUR)
library(fpc)
library(e1071)
library(klaR)
library(caret)
library(MASS)
library(randomForest)
library(class)
```
**Load data**
```{r Load data}
dataOriginal = read.csv("C:/Studymaterial/Big Data/Project/datafinal.csv")
data = dataOriginal[,]
str(data)
```
**Data preprocessing**
```{r Data preprocessing}
data.clean <- data %>%
  mutate(
    # Transform reviews to numeric
    Reviews = as.numeric(Reviews),
    # Remove currency symbol from Price, change it to numeric
    Price = as.numeric(gsub("\\$", "", as.character(Price))),
    Type=ifelse(Price==0, 0, Price),
    Type=as.factor(ifelse(Price != 0, 1, Price)),
    # Eliminate some characters to transform Installs to numeric
    Installs = gsub("\\+", "", as.character(Installs)),
    Installs = as.numeric(gsub(",", "", Installs)),
    # Eliminate M to transform Size to numeric
    Size = gsub("M", "", Size),
    # Replace cells with k to 0 since it is < 1MB
    Size = ifelse(grepl("k", Size), 1, as.numeric(Size)),
    Size = gsub("Varies with device", NA, Size),
    # Last Updated to date format
    Last.Updated = dmy(Last.Updated),
    # Replace "Varies with device" to NA since it is unknown
    Min.Android.Ver = gsub("Varies with device", NA, Minimum.Version),
    # Keep only version number to 1 decimal
    Min.Android.Ver = as.numeric(substr(Min.Android.Ver, start = 1, stop = 2)),
    # Drop old Android version column
    Minimum.Version = NULL
  )
data.clean %>%
    summarise_all(
        funs(sum(is.na(.)))
    ) %>%
  gather() %>%
  # Only show columns with NA
  filter(value> 1) %>%
  arrange(-value) %>%
    hchart('column', hcaes(x = 'key', y = 'value', color = 'key')) %>%
  hc_add_theme(hc_theme_elementary()) %>%
  hc_title(text = "Columns with NA values")
```
**Clustering with value 3**
```{r Clustering with k as 3}
data <- na.omit(data.clean)
normalize <- function(x) {
  x1 <- ((x - min(x)) / (max(x) - min(x))) * 4
  x1 <- x1 + 1
  return (x1)
}
#normalization of data
data$Size = as.numeric(data$Size)
data$Reviews = normalize(data$Reviews)
data$Installs = normalize(data$Installs)
set.seed(12345)
#k means clustering by using 3 main features taken via feature importance
k<-kmeans(data[,3:5],centers = 3, iter.max = 20, nstart = 1)
k$centers
clusterTable<-table(k$cluster)
data$classLabel = k$cluster
data$classLabel <- as.factor(data$classLabel)
clusterTable
```
**clustering plot**
```{r Cluster plot}
plotcluster(data[,3:5], k$cluster)
```
**feature importance calculation**
```{r Calculate feature importance}
#Removed 1st(Application name) and 10th(latest version) column, 
#both the columns has more than 53 categories as a factor class, 
#because of which meanDecreaseGini can not be calculated - library limitation
columns = c(2,3,4,5,6,8,9,11,12,13)
dataNew = na.omit(data[,columns])
fit_rf = randomForest(classLabel~., data=dataNew)
importance(fit_rf)
```
**Naive bayes without cross validation and feature selection**
```{r Naive bayes without CV and FS}
split = 0.6
dataForNaiveBayes = data
set.seed(123)
trainIndex <- sample(nrow(dataForNaiveBayes), split*nrow(dataForNaiveBayes), replace = FALSE)
data_train <- dataForNaiveBayes[ trainIndex,]
data_test <- dataForNaiveBayes[-trainIndex,]
modelNBfun = naiveBayes(classLabel ~ ., data_train)
predictionNB = predict(modelNBfun, data_test)
confusionMatrix(predictionNB, data_test$classLabel)
```
**Naive bayes with cross validation**
```{r Naive bayes with CV}
data_train <- na.omit(dataForNaiveBayes[ trainIndex,])
data_test <- na.omit(dataForNaiveBayes[-trainIndex,])
#Latest.updated and Latest.version has been removed, library limitation
#can not use features with factor level more than 53 categories
col <-c(2,3,4,5,6,7,8,11,12)
x<-data_train[,col]
y<-data_train$classLabel
modelNB = train(x,y,'nb',trControl=trainControl(method='cv',number=10))
predictionNB = predict(modelNB, data_test[,-13])
confusionMatrix(predictionNB, data_test$classLabel)
```
**Naive bayes with cross validation and feature selection**
```{r Naive bayes with CV and FS}
data_train <- na.omit(dataForNaiveBayes[ trainIndex,])
data_test <- na.omit(dataForNaiveBayes[-trainIndex,])
#feature selection - removed content.rating and type - low feature importance
col <-c(2,3,4,5,6,7,12)
x<-data_train[,col]
y<-data_train$classLabel
modelNB = train(x,y,'nb',trControl=trainControl(method='cv',number=10))
predictionNB = predict(modelNB, data_test[,-13])
confusionMatrix(predictionNB, data_test$classLabel)
```
**Random forest without cross validation and feature selection**
```{r Random forest without CV and FS}
dataForRandomForest = dataNew
trainIndex <- sample(nrow(dataForRandomForest), split*nrow(dataForRandomForest), replace = FALSE)
data_train <- dataForRandomForest[ trainIndex,]
data_test <- dataForRandomForest[-trainIndex,]
modelRFfun = randomForest(classLabel ~ .,data_train)
predictions <- predict(modelRFfun, data_test)
confusionMatrix(predictions, data_test$classLabel)
```
**Clustering with k=7**
```{r Clustering with k as 7}
datawith7 <- data
set.seed(12345)
#calculated clustering solution with optimal value k=7
k<-kmeans(datawith7[,3:5],centers = 7, iter.max = 20, nstart = 1)
k$centers
clusterTable<-table(k$cluster)
datawith7$classLabel = k$cluster
datawith7$classLabel <- as.factor(datawith7$classLabel)
clusterTable
```
**Plot clusters**
```{r Plot for k as 7}
plotcluster(datawith7[,3:5], k$cluster)
```
**Naive bayes with 7 clusters as class labels without CV and feature selection**
```{r Naives bayes with 7clusters}
dataForNaiveBayesFor7 <- datawith7
set.seed(123)
trainIndex <- sample(nrow(dataForNaiveBayesFor7), split*nrow(dataForNaiveBayesFor7), replace = FALSE)
data_train <- na.omit(dataForNaiveBayesFor7[ trainIndex,])
data_test <- na.omit(dataForNaiveBayesFor7[-trainIndex,])
#Latest.updated and Latest.version has been removed, library limitation
modelNBfunFor7 = naiveBayes(classLabel ~ ., data_train)
predictionNB = predict(modelNBfunFor7, data_test)
confusionMatrix(predictionNB, data_test$classLabel)
```
**Naive bayes with cross validation for 7 cluster value**
```{r Naive bayes with CV for k as 7}
#application name, (1st), Latest.updated(9th) and Latest.version(10th) has been removed, library limitation
col <-c(2,3,4,5,6,7,8,11,12)
x<-data_train[,col]
y<-data_train$classLabel
modelNBF7 = train(x,y,'nb',trControl=trainControl(method='cv',number=10))
predictionNBF7 = predict(modelNBF7, data_test[,-13])
confusionMatrix(predictionNBF7, data_test$classLabel)
```
**Random forest for 7clusters**
```{r Random forest with k as 7}
#9th column(Last.updated) can be added again, as date format works in random forest.
columns = c(2,3,4,5,6,8,9,11,12,13)
dataForRandomForestFor7 = datawith7[,columns]
trainIndex <- sample(nrow(dataForRandomForestFor7), split*nrow(dataForRandomForestFor7), replace = FALSE)
data_train <- dataForRandomForestFor7[ trainIndex,]
data_test <- dataForRandomForestFor7[-trainIndex,]
modelRFfun = randomForest(classLabel ~ .,data_train)
predictions <- predict(modelRFfun, data_test)
confusionMatrix(predictions, data_test$classLabel)
```
**K nearest neighbor**
```{r KNN}
#KNN requires all numeric features, hence all important features have been considered for this algorithm.
dataForKNNFor7 = datawith7
dataForKNNFor7$Category = as.numeric(dataForKNNFor7$Category)
columns <- c(2,3,4,5,6,13)
dataForKNNFor7 = dataForKNNFor7[,columns]
trainIndex <- sample(nrow(dataForKNNFor7), split*nrow(dataForKNNFor7), replace = FALSE)
data_train <- na.omit(dataForKNNFor7[ trainIndex,])
data_test <- dataForKNNFor7[-trainIndex,]
predictions = knn(data_train, data_test,cl=data_train$classLabel,k=11)
confusionMatrix(predictions, data_test$classLabel)
```
**Popular categories with respect to number of installs**
```{r Popular Category wrt NumOfInstalls}
graphData <- data.clean
graphData %>%
  count(Category, Installs) %>%
  group_by(Category) %>%
  summarize(
    TotalInstalls = sum(as.numeric(Installs))
  ) %>%
  arrange(-TotalInstalls) %>%
  hchart('scatter', hcaes(x = "Category", y = "TotalInstalls", size = "TotalInstalls", color = "Category")) %>%
  hc_add_theme(hc_theme_538()) %>%
  hc_title(text = "Most popular categories (# of installs)")
```
**Popular category with respect to average rating**
```{r Categories wrt mean rating}
graphData %>%
  count(Category, Rating) %>%
  group_by(Category) %>%
  summarize(
    Rating = mean(Rating)
  ) %>%
  arrange(-Rating) %>%
  hchart('scatter', hcaes(x = "Category", y = "Rating", size = "Rating", color = "Category")) %>%
  hc_add_theme(hc_theme_538()) %>%
  hc_title(text = "Categories with their mean rating")
```
**Distribution of application size**
```{r Dist of app size}
graphData %>%
  count(Size) %>%
  hchart('area', hcaes(x = "Size", y = "n")) %>%
  hc_colors("#fb4901") %>%
  hc_add_theme(hc_theme_ffx()) %>%
  hc_title(text = "Distribution of application size (in MB)")
```
**Number of applications for each installation category**
```{r NumOfApp for each InstallationCat}
tmp <- graphData %>%
  group_by(
    Installs.Group = cut(Installs, breaks= seq(0, 1000000000, by = 10000))
    ) %>% 
  summarise(
    n= n()
    )

highchart() %>%
  hc_chart(
    type = "pie"
    ) %>%
  hc_add_series_labels_values(
    labels = tmp$Installs.Group, values = tmp$n
    ) %>%
  hc_title(
    text="Number of installs (groups per 10k)"
    ) %>%
  hc_add_theme(hc_theme_economist())
```
**Percentage of paid vs free applications**
```{r Paid per free apps}
tmp <- graphData %>%
  count(Type) %>%
  mutate(perc = round((n /sum(n))*100)) %>%
  arrange(desc(perc))

    hciconarray(tmp$Type, tmp$perc, icons = "android", size = 5) %>%
  hc_title(text="Percentage of paid vs free apps")
```
**Percentage of paid vs free applications per category**
```{r Per of paid vs free by cat}
graphData %>% 
  group_by(Category, Type) %>%
  summarize(
    n = n()
  ) %>%
  mutate(perc = round((n /sum(n))*100)) %>%
  hchart('bar', hcaes(x = 'Category', y = 'perc', group = 'Type')) %>%
  hc_plotOptions(series=list(stacking='normal')) %>%
  hc_title(text="Percentage of Free vs Paid by Category") %>%
  hc_add_theme(hc_theme_flat())
```
**Median price per category**
```{r Price per category}
graphData %>%
  filter(Type == 1) %>%
  group_by(Category) %>%
  summarize(
    Price = median(Price)
  ) %>%
  arrange(-Price) %>%
  hchart('treemap', hcaes(x = 'Category', value = 'Price', color = 'Price')) %>%
  hc_add_theme(hc_theme_elementary()) %>%
  hc_title(text="Median price per category")
```
**Total revenue generated by each category**
```{r Revenu generated}
graphData %>%
  filter(Type == 1) %>%
  mutate(
    Total.Paid = Price * Installs
  ) %>%
  group_by(Category) %>%
  summarize(USD.Paid = sum(Total.Paid)) %>%
  arrange(-USD.Paid) %>%
  hchart('treemap', hcaes(x = 'Category', value = 'USD.Paid', color = 'USD.Paid')) %>%
  hc_add_theme(hc_theme_elementary()) %>%
  hc_title(text="Total amount spent by category (installs * price)")
```
**Number of installation by audience**
```{r Number of installs by age}
tmp <- graphData %>%
  group_by(Content.Rating) %>%
  summarize(Total.Installs = sum(Installs)) %>%
  arrange(-Total.Installs)
highchart() %>% 
  hc_chart(type ="column",
           options3d = list(enabled = TRUE, alpha = 15, beta = 15)) %>%
  hc_xAxis(categories = tmp$Content.Rating) %>% 
  hc_add_series(data = tmp$Total.Installs, name = "Total.Installs") %>%
  hc_add_theme(hc_theme_smpl()) %>%
  hc_title(
    text="Number of Installs by audience (all apps)"
    ) %>%
    hc_chart(
      borderColor = '#EBBA95',
      borderRadius = 10,
      borderWidth = 1,
      backgroundColor = list(
        linearGradient = c(0, 0, 500, 500), stops = list(
               list(0, 'rgb(255, 255, 255)'),
               list(1, 'rgb(180, 180, 255)')
             )))
```
**number of applications by last updated date**
```{r Last updated date }
tmp <- graphData %>% count(Last.Updated)

# Transform data into time series
time_series <- xts(
  tmp$n, order.by = tmp$Last.Updated 
)

highchart(type = "stock") %>% 
  hc_title(text = "Last updated date") %>% 
  hc_subtitle(text = "Number of applications by date of last update") %>% 
  hc_add_series(time_series) %>%
  hc_add_theme(hc_theme_gridlight())

rm(time_series)
```
**Number of installation per Minimum android version with respect to application type**
```{r Min android ver}
graphData %>%
 filter(Min.Android.Ver > 0, Type %in% c(0, 1)
   ) %>%
 group_by(as.factor(Min.Android.Ver), Type) %>%
 rename(Minimum.Android.Version = "as.factor(Min.Android.Ver)") %>%
 summarize(Total.Installs = sum(Installs)) %>%
 hchart(
   type = "heatmap", hcaes(x = Minimum.Android.Version, y = Type, value = Total.Installs)
   ) %>%
 hc_title(text = "Minimum Android Version (by number of installs)")
```
**Top 10 applications**
```{r Top 10app}
graphData %>%
    dplyr::select(App.Name, Installs, Category) %>%
    arrange(-Installs) %>%
    head(10)
```

